186:@0.054582:0.966558:0.078778:0.966558:0.078778:0.950778:0.054582:0.950778:0.000000:0.000000:0.000000
Integral definida. Propiedades:@0.404235:0.117815:0.779706:0.117815:0.779706:0.073156:0.404235:0.073156:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
M.5.1.65. Aplicar la interpretación geométrica de la integral de una función escalonada no negativa como la superficie limitada por la curva y el eje x. :@0.140997:0.940354:0.783367:0.940354:0.783367:0.930312:0.140997:0.930312:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
M.5.1.66. Calcular la integral definida de una función polinomial de grado ≤ 4 aproximando el cálculo como una sucesión de funciones escalonadas.:@0.140997:0.949155:0.778030:0.949155:0.778030:0.939113:0.140997:0.939113:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
M.5.1.63. Realizar las operaciones de suma y multiplicación de funciones escalonadas y de multiplicación de números reales por funciones escalonadas aplicando las :@0.140997:0.957956:0.880578:0.957956:0.880578:0.947914:0.140997:0.947914:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
propiedades de los números reales.:@0.140997:0.966757:0.292116:0.966757:0.292116:0.956715:0.140997:0.956715:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Saberes previos:@0.199646:0.115710:0.307805:0.115710:0.307805:0.100238:0.199646:0.100238:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
¿Qué es la integral?:@0.199884:0.144338:0.322627:0.144338:0.322627:0.129274:0.199884:0.129274:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Desequilibrio cognitivo:@0.199646:0.191489:0.363493:0.191489:0.363493:0.176016:0.199646:0.176016:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
¿En qué consiste el teo-:@0.199884:0.220118:0.350437:0.220118:0.350437:0.205054:0.199884:0.205054:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
rema fundamental del cálculo?:@0.153341:0.235960:0.352370:0.235960:0.352370:0.220896:0.153341:0.220896:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Recuerda que…:@0.199646:0.416910:0.309406:0.416910:0.309406:0.401438:0.199646:0.401438:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
  Aunque el símbolo :@0.199884:0.445538:0.341237:0.445538:0.341237:0.430475:0.199884:0.430475:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
sumatorio ya fue tratado en :@0.153341:0.461380:0.337981:0.461380:0.337981:0.446317:0.153341:0.446317:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
unidades anteriores, volvemos :@0.153341:0.477222:0.352755:0.477222:0.352755:0.462159:0.153341:0.462159:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a revisar algunos resultados :@0.153341:0.493064:0.333461:0.493064:0.333461:0.478001:0.153341:0.478001:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
importantes. Supongamos :@0.153341:0.508906:0.329501:0.508906:0.329501:0.493843:0.153341:0.493843:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
que se tiene   números reales :@0.153341:0.524748:0.348834:0.524748:0.348834:0.509685:0.153341:0.509685:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
n:@0.235117:0.524853:0.243665:0.524853:0.243665:0.509817:0.235117:0.509817:0.000000
z:@0.153341:0.540695:0.159409:0.540695:0.159409:0.525659:0.153341:0.525659:0.000000
1:@0.159415:0.543583:0.163937:0.543583:0.163937:0.534801:0.159415:0.534801:0.000000
, …  . A la suma: :@0.163936:0.540590:0.275692:0.540590:0.275692:0.525527:0.163936:0.525527:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
z:@0.187753:0.540695:0.193822:0.540695:0.193822:0.525659:0.187753:0.525659:0.000000
n:@0.193875:0.543644:0.198858:0.543644:0.198858:0.534878:0.193875:0.534878:0.000000
z:@0.153353:0.556537:0.159422:0.556537:0.159422:0.541501:0.153353:0.541501:0.000000
1:@0.159415:0.559425:0.163937:0.559425:0.163937:0.550643:0.159415:0.550643:0.000000
 +   + …  la expresamos en:@0.163936:0.556432:0.351513:0.556432:0.351513:0.541369:0.163936:0.541369:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
z:@0.181368:0.556537:0.187437:0.556537:0.187437:0.541501:0.181368:0.541501:0.000000
2:@0.187437:0.559425:0.191959:0.559425:0.191959:0.550643:0.187437:0.550643:0.000000
z:@0.226910:0.556537:0.232978:0.556537:0.232978:0.541501:0.226910:0.541501:0.000000
n :@0.232978:0.559425:0.240310:0.559425:0.240310:0.550643:0.232978:0.550643:0.000000:0.000000
forma abreviada como:       ,:@0.153346:0.579403:0.336296:0.579403:0.336296:0.564340:0.153346:0.564340:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
z:@0.325253:0.579508:0.331321:0.579508:0.331321:0.564472:0.325253:0.564472:0.000000
j:@0.331320:0.582456:0.333371:0.582456:0.333371:0.573690:0.331320:0.573690:0.000000
que se lee “suma de los   con   :@0.153342:0.602374:0.354237:0.602372:0.354237:0.587309:0.153342:0.587310:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
z:@0.306233:0.602479:0.312302:0.602479:0.312302:0.587442:0.306233:0.587442:0.000000
j:@0.312304:0.605426:0.314355:0.605426:0.314355:0.596659:0.312304:0.596659:0.000000
j:@0.346937:0.602478:0.350455:0.602478:0.350455:0.587441:0.346937:0.587441:0.000000
que varía de 1 a  ”. Es decir,:@0.153341:0.618214:0.328290:0.618214:0.328290:0.603151:0.153341:0.603151:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
n:@0.258371:0.618320:0.266920:0.618320:0.266920:0.603283:0.258371:0.603283:0.000000
       =   +   + … +  .:@0.184564:0.641185:0.330279:0.641184:0.330279:0.626121:0.184564:0.626122:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
z:@0.203473:0.641291:0.209541:0.641291:0.209541:0.626254:0.203473:0.626254:0.000000
j:@0.209543:0.644239:0.211594:0.644239:0.211594:0.635472:0.209543:0.635472:0.000000
z:@0.229436:0.641290:0.235504:0.641290:0.235504:0.626253:0.229436:0.626253:0.000000
1:@0.235504:0.644177:0.240027:0.644177:0.240027:0.635395:0.235504:0.635395:0.000000
z:@0.257458:0.641290:0.263526:0.641290:0.263526:0.626253:0.257458:0.626253:0.000000
2:@0.263526:0.644177:0.268049:0.644177:0.268049:0.635395:0.263526:0.635395:0.000000
z:@0.316649:0.641290:0.322717:0.641290:0.322717:0.626253:0.316649:0.626253:0.000000
n:@0.322717:0.644177:0.327845:0.644177:0.327845:0.635395:0.322717:0.635395:0.000000
Al símbolo      se le llama suma-:@0.153341:0.671284:0.357209:0.671284:0.357209:0.656221:0.153341:0.656221:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
torio; a   se le llama término :@0.153341:0.687126:0.341098:0.687124:0.341098:0.672061:0.153341:0.672063:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
z:@0.202188:0.687231:0.208257:0.687231:0.208257:0.672195:0.202188:0.672195:0.000000
j:@0.208262:0.690178:0.210313:0.690178:0.210313:0.681411:0.208262:0.681411:0.000000
general de la suma;   es el índice :@0.153344:0.702966:0.361379:0.702966:0.361379:0.687903:0.153344:0.687903:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
j:@0.279816:0.703072:0.283334:0.703072:0.283334:0.688035:0.279816:0.688035:0.000000
de sumación;   = 1 y  =   son :@0.153344:0.718808:0.346936:0.718808:0.346936:0.703745:0.153344:0.703745:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
j:@0.242999:0.718914:0.246516:0.718914:0.246516:0.703877:0.242999:0.703877:0.000000
j  n:@0.286411:0.718914:0.315909:0.718914:0.315909:0.703877:0.286411:0.703877:0.000000:0.000000:0.000000:0.000000
los límites de sumación (esto es, :@0.153344:0.734650:0.364491:0.734650:0.364491:0.719587:0.153344:0.719587:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
j:@0.153344:0.750598:0.156862:0.750598:0.156862:0.735561:0.153344:0.735561:0.000000
 varía de 1 hasta  ).:@0.156862:0.750492:0.281116:0.750492:0.281116:0.735429:0.156862:0.735429:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
n:@0.264617:0.750598:0.273165:0.750598:0.273165:0.735561:0.264617:0.735561:0.000000
El índice de sumación se puede :@0.153344:0.773463:0.360533:0.773463:0.360533:0.758400:0.153344:0.758400:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
representar con cualquier letra :@0.153344:0.789305:0.354816:0.789305:0.354816:0.774242:0.153344:0.774242:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
minúscula, aunque se prefieren :@0.153344:0.805147:0.358723:0.805147:0.358723:0.790084:0.153344:0.790084:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
i j k l:@0.153344:0.821095:0.190213:0.821095:0.190213:0.806058:0.153344:0.806058:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
,  ,  ,  .:@0.156809:0.820989:0.192728:0.820989:0.192728:0.805926:0.156809:0.805926:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
∑:@0.306957:0.580927:0.320997:0.580927:0.320997:0.557351:0.306957:0.557351:0.000000
n:@0.311919:0.563246:0.316902:0.563246:0.316902:0.554480:0.311919:0.554480:0.000000
j:@0.308248:0.586126:0.310299:0.586126:0.310299:0.577360:0.308248:0.577360:0.000000
=1:@0.310299:0.586065:0.320574:0.586065:0.320574:0.577283:0.310299:0.577283:0.000000:0.000000
∑:@0.189583:0.643003:0.203623:0.643003:0.203623:0.619428:0.189583:0.619428:0.000000
n:@0.194545:0.625322:0.199528:0.625322:0.199528:0.616556:0.194545:0.616556:0.000000
j:@0.190874:0.648203:0.192925:0.648203:0.192925:0.639437:0.190874:0.639437:0.000000
=1:@0.192925:0.648141:0.203200:0.648141:0.203200:0.639360:0.192925:0.639360:0.000000:0.000000
∑:@0.229360:0.673522:0.243400:0.673522:0.243400:0.649946:0.229360:0.649946:0.000000
Propiedades de la sumatoria:@0.404236:0.147639:0.631674:0.147639:0.631674:0.129956:0.404236:0.129956:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Dados      ,  ,      ,   = 1, …,  ,       . Se verifican las siguientes :@0.404236:0.164346:0.895939:0.164346:0.895939:0.147849:0.404236:0.147849:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
n:@0.453979:0.164462:0.463342:0.164462:0.463342:0.147993:0.453979:0.147993:0.000000
:@0.467218:0.163828:0.481871:0.163828:0.481871:0.150454:0.467218:0.150454:0.000000
Z:@0.485757:0.163259:0.498048:0.163259:0.498048:0.150397:0.485757:0.150397:0.000000
+:@0.498048:0.156737:0.504349:0.156737:0.504349:0.147119:0.498048:0.147119:0.000000
v w:@0.510995:0.164462:0.540014:0.164462:0.540014:0.147993:0.510995:0.147993:0.000000:0.000000:0.000000
j:@0.518906:0.167692:0.521153:0.167692:0.521153:0.158090:0.518906:0.158090:0.000000
j:@0.540142:0.167692:0.542388:0.167692:0.542388:0.158090:0.540142:0.158090:0.000000
:@0.546273:0.163828:0.560926:0.163828:0.560926:0.150454:0.546273:0.150454:0.000000
:@0.564810:0.163259:0.578114:0.163259:0.578114:0.150397:0.564810:0.150397:0.000000
j:@0.584761:0.164462:0.588614:0.164462:0.588614:0.147993:0.584761:0.147993:0.000000
n:@0.644040:0.164462:0.653403:0.164462:0.653403:0.147993:0.644040:0.147993:0.000000
α:@0.663895:0.171420:0.673992:0.171420:0.673992:0.153285:0.663895:0.153285:0.000000
:@0.677880:0.163828:0.692532:0.163828:0.692532:0.150454:0.677880:0.150454:0.000000
:@0.696418:0.163259:0.709723:0.163259:0.709723:0.150397:0.696418:0.150397:0.000000
propiedades.:@0.404234:0.181697:0.495607:0.181697:0.495607:0.165199:0.404234:0.165199:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
i):@0.404234:0.216615:0.414772:0.216615:0.414772:0.199901:0.404234:0.199901:0.000000:0.000000
      (  +  ) =       +      . :@0.414772:0.216398:0.603278:0.216398:0.603278:0.199901:0.414772:0.199901:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
v:@0.450490:0.216514:0.458273:0.216514:0.458273:0.200045:0.450490:0.200045:0.000000
j:@0.458418:0.219744:0.460665:0.219744:0.460665:0.210143:0.458418:0.210143:0.000000
w:@0.479757:0.216514:0.491971:0.216514:0.491971:0.200045:0.479757:0.200045:0.000000
j:@0.492104:0.219744:0.494351:0.219744:0.494351:0.210143:0.492104:0.210143:0.000000
v:@0.535964:0.216514:0.543747:0.216514:0.543747:0.200045:0.535964:0.200045:0.000000
j:@0.543881:0.219744:0.546127:0.219744:0.546127:0.210143:0.543881:0.210143:0.000000
w:@0.581787:0.216514:0.594001:0.216514:0.594001:0.200045:0.581787:0.200045:0.000000
j:@0.594135:0.219744:0.596381:0.219744:0.596381:0.210143:0.594135:0.210143:0.000000
ii):@0.645469:0.216615:0.660265:0.216615:0.660265:0.199901:0.645469:0.199901:0.000000:0.000000:0.000000
        (:@0.660265:0.216398:0.699354:0.216398:0.699354:0.199901:0.660265:0.199901:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
α :@0.699355:0.223473:0.713321:0.223473:0.713321:0.205337:0.699355:0.205337:0.000000:0.000000
v:@0.713328:0.216514:0.721111:0.216514:0.721111:0.200045:0.713328:0.200045:0.000000
j:@0.721247:0.219744:0.723493:0.219744:0.723493:0.210143:0.721247:0.210143:0.000000
) =       .:@0.724055:0.216398:0.789472:0.216398:0.789472:0.199901:0.724055:0.199901:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
α:@0.749098:0.223473:0.759194:0.223473:0.759194:0.205337:0.749098:0.205337:0.000000
v:@0.775767:0.216514:0.783551:0.216514:0.783551:0.200045:0.775767:0.200045:0.000000
j:@0.783685:0.219744:0.785931:0.219744:0.785931:0.210143:0.783685:0.210143:0.000000
iii):@0.404244:0.258445:0.423297:0.258445:0.423297:0.241731:0.404244:0.241731:0.000000:0.000000:0.000000:0.000000
     (:@0.423297:0.258228:0.450500:0.258228:0.450500:0.241731:0.423297:0.241731:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
v:@0.450500:0.258344:0.458283:0.258344:0.458283:0.241875:0.450500:0.241875:0.000000
j:@0.458418:0.261573:0.460665:0.261573:0.460665:0.251972:0.458418:0.251972:0.000000
+1:@0.461226:0.261506:0.472480:0.261506:0.472480:0.251887:0.461226:0.251887:0.000000:0.000000
 –  ) =   –  .:@0.472480:0.258229:0.574664:0.258229:0.574664:0.241731:0.472480:0.241731:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
v:@0.491264:0.258345:0.499047:0.258345:0.499047:0.241876:0.491264:0.241876:0.000000
j:@0.499180:0.261573:0.501427:0.261573:0.501427:0.251972:0.499180:0.251972:0.000000
v:@0.527033:0.258345:0.534816:0.258345:0.534816:0.241876:0.527033:0.241876:0.000000
n:@0.534932:0.261573:0.540390:0.261573:0.540390:0.251972:0.534932:0.251972:0.000000
v:@0.559173:0.258345:0.566956:0.258345:0.566956:0.241876:0.559173:0.241876:0.000000
1:@0.566956:0.261506:0.571909:0.261506:0.571909:0.251887:0.566956:0.251887:0.000000
Las expresiones más usadas en el cálculo de integrales definidas son::@0.404244:0.300059:0.886424:0.300059:0.886424:0.283561:0.404244:0.283561:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1.:@0.404244:0.334977:0.416516:0.334977:0.416516:0.318262:0.404244:0.318262:0.000000:0.000000
  Para todo       y      ,       =  . Nota que     1 =  . :@0.416516:0.334760:0.822774:0.334760:0.822774:0.318262:0.416516:0.318262:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
n:@0.501726:0.334876:0.511089:0.334876:0.511089:0.318407:0.501726:0.318407:0.000000
:@0.515231:0.334241:0.529883:0.334241:0.529883:0.320868:0.515231:0.320868:0.000000
Z:@0.534025:0.333673:0.546317:0.333673:0.546317:0.320810:0.534025:0.320810:0.000000
+:@0.546317:0.327149:0.552618:0.327149:0.552618:0.317531:0.546317:0.317531:0.000000
a:@0.568723:0.334875:0.577701:0.334875:0.577701:0.318406:0.568723:0.318406:0.000000
:@0.581842:0.334241:0.596494:0.334241:0.596494:0.320868:0.581842:0.320868:0.000000
:@0.600636:0.333673:0.613941:0.333673:0.613941:0.320810:0.600636:0.320810:0.000000
a an:@0.637406:0.334875:0.683662:0.334875:0.683662:0.318406:0.637406:0.318406:0.000000:0.000000:0.000000:0.000000
n:@0.806515:0.334875:0.815877:0.334875:0.815877:0.318406:0.806515:0.318406:0.000000
2.:@0.404239:0.369678:0.416511:0.369678:0.416511:0.352963:0.404239:0.352963:0.000000:0.000000
  Sea      , calculemos la suma de los   primeros números naturales: :@0.416511:0.369461:0.895899:0.369461:0.895899:0.352963:0.416511:0.352963:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
n:@0.454694:0.369577:0.464057:0.369577:0.464057:0.353108:0.454694:0.353108:0.000000
:@0.467056:0.368942:0.481708:0.368942:0.481708:0.355569:0.467056:0.355569:0.000000
N:@0.484715:0.368374:0.499051:0.368374:0.499051:0.355512:0.484715:0.355512:0.000000
n:@0.683694:0.369577:0.693057:0.369577:0.693057:0.353108:0.683694:0.353108:0.000000
 :@0.404236:0.393940:0.408378:0.393940:0.408378:0.377442:0.404236:0.377442:0.000000
S:@0.559437:0.394056:0.567317:0.394056:0.567317:0.377587:0.559437:0.377587:0.000000
n:@0.567237:0.397285:0.572696:0.397285:0.572696:0.387684:0.567237:0.387684:0.000000
 =       = 0 + 1 + 2 + … +  .:@0.572695:0.393939:0.760319:0.393939:0.760319:0.377442:0.572695:0.377442:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
j:@0.608355:0.394055:0.612208:0.394055:0.612208:0.377586:0.608355:0.377586:0.000000
n:@0.748201:0.394055:0.757564:0.394055:0.757564:0.377586:0.748201:0.377586:0.000000
Para     , se tiene (  + 1)  –   =   + 2  + 1 –   = 2  + 1. :@0.427974:0.428641:0.823301:0.428641:0.823301:0.412143:0.427974:0.412143:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
j:@0.462459:0.428757:0.466312:0.428757:0.466312:0.412288:0.462459:0.412288:0.000000
:@0.470075:0.428122:0.484727:0.428122:0.484727:0.414749:0.470075:0.414749:0.000000
N:@0.488499:0.427554:0.502836:0.427554:0.502836:0.414692:0.488499:0.414692:0.000000
j:@0.573914:0.428757:0.577767:0.428757:0.577767:0.412288:0.573914:0.412288:0.000000
2:@0.611306:0.422357:0.616012:0.422357:0.616012:0.412755:0.611306:0.412755:0.000000
j:@0.634795:0.428757:0.638648:0.428757:0.638648:0.412288:0.634795:0.412288:0.000000
2:@0.638647:0.422357:0.643354:0.422357:0.643354:0.412755:0.638647:0.412755:0.000000
j:@0.662447:0.428757:0.666300:0.428757:0.666300:0.412288:0.662447:0.412288:0.000000
2:@0.666299:0.422357:0.671005:0.422357:0.671005:0.412755:0.666299:0.412755:0.000000
j:@0.698593:0.428757:0.702446:0.428757:0.702446:0.412288:0.698593:0.412288:0.000000
j:@0.748817:0.428757:0.752670:0.428757:0.752670:0.412288:0.748817:0.412288:0.000000
2:@0.752669:0.422357:0.757375:0.422357:0.757375:0.412755:0.752669:0.412755:0.000000
j:@0.784963:0.428757:0.788816:0.428757:0.788816:0.412288:0.784963:0.412288:0.000000
 :@0.404243:0.445992:0.408385:0.445992:0.408385:0.429494:0.404243:0.429494:0.000000
 :@0.404243:0.463342:0.408385:0.463342:0.408385:0.446845:0.404243:0.446845:0.000000
Por la propiedad iii), se obtiene::@0.427978:0.463342:0.650237:0.463342:0.650237:0.446845:0.427978:0.446845:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.404243:0.487821:0.408385:0.487821:0.408385:0.471324:0.404243:0.471324:0.000000
     [(  + 1)  –  ] = (  + 1) ,:@0.567323:0.487821:0.752436:0.487822:0.752436:0.471324:0.567323:0.471324:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
j:@0.600999:0.487937:0.604852:0.487937:0.604852:0.471468:0.600999:0.471468:0.000000
2:@0.638383:0.481469:0.643336:0.481469:0.643336:0.471851:0.638383:0.471851:0.000000
j:@0.662118:0.487938:0.665971:0.487938:0.665971:0.471469:0.662118:0.471469:0.000000
2:@0.665972:0.481469:0.670925:0.481469:0.670925:0.471851:0.665972:0.471851:0.000000
n:@0.701826:0.487938:0.711189:0.487938:0.711189:0.471469:0.701826:0.471469:0.000000
2:@0.744729:0.481469:0.749682:0.481469:0.749682:0.471851:0.744729:0.471851:0.000000
 :@0.404235:0.505173:0.408377:0.505173:0.408377:0.488675:0.404235:0.488675:0.000000
 :@0.404235:0.522524:0.408377:0.522524:0.408377:0.506026:0.404235:0.506026:0.000000
y por las propiedades i) y ii), resulta que::@0.427970:0.522524:0.711549:0.522524:0.711549:0.506026:0.427970:0.506026:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
(  + 1)  =     [(  + 1)  –  ] =    (2  + 1) = 2      +    1 = 2    :@0.427970:0.547003:0.822899:0.547002:0.822899:0.530504:0.427970:0.530505:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
n:@0.433923:0.547118:0.443286:0.547118:0.443286:0.530650:0.433923:0.530650:0.000000
2:@0.476836:0.540649:0.481789:0.540649:0.481789:0.531031:0.476836:0.531031:0.000000
j:@0.530414:0.547118:0.534267:0.547118:0.534267:0.530649:0.530414:0.530649:0.000000
2:@0.567807:0.540649:0.572760:0.540649:0.572760:0.531031:0.567807:0.531031:0.000000
j:@0.591542:0.547118:0.595395:0.547118:0.595395:0.530649:0.591542:0.530649:0.000000
2:@0.595396:0.540649:0.600349:0.540649:0.600349:0.531031:0.595396:0.531031:0.000000
j:@0.653326:0.547118:0.657179:0.547118:0.657179:0.530649:0.653326:0.530649:0.000000
j:@0.734876:0.547118:0.738729:0.547118:0.738729:0.530649:0.734876:0.530649:0.000000
j + n:@0.822899:0.547118:0.855283:0.547118:0.855283:0.530649:0.822899:0.530649:0.000000:0.000000:0.000000:0.000000:0.000000
 + 1,:@0.855283:0.547002:0.885626:0.547002:0.885626:0.530504:0.855283:0.530504:0.000000:0.000000:0.000000:0.000000:0.000000
donde::@0.427963:0.577178:0.477609:0.577178:0.477609:0.560680:0.427963:0.560680:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.404228:0.601657:0.408370:0.601657:0.408370:0.585159:0.404228:0.585159:0.000000
2     :@0.546521:0.601657:0.575727:0.601657:0.575727:0.585159:0.546521:0.585159:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
j =  n       n   :@0.577654:0.601773:0.690914:0.601771:0.690914:0.585303:0.577654:0.585304:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
( +1) – –1 =  ( +1),:@0.599038:0.601657:0.773215:0.601656:0.773215:0.585158:0.599038:0.585159:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.644055:0.595304:0.649008:0.595304:0.649008:0.585686:0.644055:0.585686:0.000000
n n   :@0.716286:0.601771:0.757842:0.601771:0.757842:0.585303:0.716286:0.585303:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.404247:0.636357:0.408389:0.636357:0.408389:0.619859:0.404247:0.619859:0.000000
S:@0.534692:0.636473:0.542572:0.636473:0.542572:0.620004:0.534692:0.620004:0.000000
n:@0.542482:0.639703:0.547941:0.639703:0.547941:0.630101:0.542482:0.630101:0.000000
 =       = 0+1+2+…   =                .  :@0.547940:0.636357:0.792975:0.636357:0.792975:0.619859:0.547940:0.619859:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
j:@0.581481:0.636473:0.585334:0.636473:0.585334:0.620004:0.581481:0.620004:0.000000
            n:@0.611958:0.636473:0.704759:0.636473:0.704759:0.620004:0.611958:0.620004:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
   :@0.404240:0.653708:0.416666:0.653708:0.416666:0.637210:0.404240:0.637210:0.000000:0.000000:0.000000
3.:@0.404240:0.671276:0.416512:0.671276:0.416512:0.654561:0.404240:0.654561:0.000000:0.000000
  Calculemos la suma de los cuadrados de los   primeros números :@0.416512:0.671059:0.895863:0.671059:0.895863:0.654561:0.416512:0.654561:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
n:@0.746694:0.671174:0.756057:0.671174:0.756057:0.654706:0.746694:0.654706:0.000000
naturales: :@0.427975:0.688409:0.499546:0.688409:0.499546:0.671912:0.427975:0.671912:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.404240:0.714667:0.408382:0.714667:0.408382:0.698169:0.404240:0.698169:0.000000
S:@0.546957:0.714783:0.554837:0.714783:0.554837:0.698314:0.546957:0.698314:0.000000
n:@0.554758:0.718015:0.560217:0.718015:0.560217:0.708414:0.554758:0.708414:0.000000
 =       = 0  + 1  + 2  + … +  .:@0.560216:0.714671:0.772795:0.714671:0.772795:0.698173:0.560216:0.698173:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
j:@0.595876:0.714786:0.599729:0.714786:0.599729:0.698318:0.595876:0.698318:0.000000
2:@0.599921:0.708318:0.604874:0.708318:0.604874:0.698700:0.599921:0.698700:0.000000
2:@0.632461:0.708318:0.637414:0.708318:0.637414:0.698700:0.632461:0.698700:0.000000
2:@0.665002:0.708318:0.669955:0.708318:0.669955:0.698700:0.665002:0.698700:0.000000
2:@0.697542:0.708318:0.702495:0.708318:0.702495:0.698700:0.697542:0.698700:0.000000
n:@0.755726:0.714786:0.765089:0.714786:0.765089:0.698318:0.755726:0.698318:0.000000
2:@0.765088:0.708318:0.770041:0.708318:0.770041:0.698700:0.765088:0.698700:0.000000
 :@0.404231:0.732021:0.408373:0.732021:0.408373:0.715524:0.404231:0.715524:0.000000
Para      se tiene (  + 1)  –   =   + 3  + 3  + 1 –   = 3  + 3  + 1.:@0.427966:0.749372:0.888942:0.749372:0.888942:0.732874:0.427966:0.732874:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
j:@0.462451:0.749488:0.466304:0.749488:0.466304:0.733019:0.462451:0.733019:0.000000
:@0.470075:0.748853:0.484727:0.748853:0.484727:0.735480:0.470075:0.735480:0.000000
N:@0.488499:0.748285:0.502836:0.748285:0.502836:0.735423:0.488499:0.735423:0.000000
j:@0.571157:0.749488:0.575010:0.749488:0.575010:0.733019:0.571157:0.733019:0.000000
3:@0.608552:0.743019:0.613505:0.743019:0.613505:0.733401:0.608552:0.733401:0.000000
j:@0.632287:0.749488:0.636140:0.749488:0.636140:0.733019:0.632287:0.733019:0.000000
3:@0.636141:0.743087:0.640847:0.743087:0.640847:0.733485:0.636141:0.733485:0.000000
j:@0.659939:0.749488:0.663792:0.749488:0.663792:0.733019:0.659939:0.733019:0.000000
3:@0.663791:0.743087:0.668497:0.743087:0.668497:0.733485:0.663791:0.733485:0.000000
j:@0.696085:0.749488:0.699938:0.749488:0.699938:0.733019:0.696085:0.733019:0.000000
2:@0.699938:0.743087:0.704644:0.743087:0.704644:0.733485:0.699938:0.733485:0.000000
j:@0.732231:0.749488:0.736084:0.749488:0.736084:0.733019:0.732231:0.733019:0.000000
j:@0.782456:0.749488:0.786309:0.749488:0.786309:0.733019:0.782456:0.733019:0.000000
3:@0.786306:0.743087:0.791013:0.743087:0.791013:0.733485:0.786306:0.733485:0.000000
j:@0.818602:0.749488:0.822455:0.749488:0.822455:0.733019:0.818602:0.733019:0.000000
2:@0.822453:0.743087:0.827159:0.743087:0.827159:0.733485:0.822453:0.733485:0.000000
j:@0.854747:0.749488:0.858600:0.749488:0.858600:0.733019:0.854747:0.733019:0.000000
 :@0.404229:0.784074:0.408371:0.784074:0.408371:0.767576:0.404229:0.767576:0.000000
Por la propiedad iii), resulta que::@0.427963:0.784074:0.655290:0.784074:0.655290:0.767576:0.427963:0.767576:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.404229:0.808553:0.408371:0.808553:0.408371:0.792055:0.404229:0.792055:0.000000
    [(  + 1)  –  ] = (  + 1) ,:@0.569370:0.808553:0.750365:0.808552:0.750365:0.792054:0.569370:0.792055:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
j:@0.598904:0.808668:0.602757:0.808668:0.602757:0.792200:0.598904:0.792200:0.000000
3:@0.636310:0.802199:0.641264:0.802199:0.641264:0.792581:0.636310:0.792581:0.000000
j:@0.660048:0.808668:0.663901:0.808668:0.663901:0.792199:0.660048:0.792199:0.000000
3:@0.663900:0.802199:0.668853:0.802199:0.668853:0.792581:0.663900:0.792581:0.000000
n:@0.699755:0.808668:0.709118:0.808668:0.709118:0.792199:0.699755:0.792199:0.000000
3:@0.742658:0.802199:0.747611:0.802199:0.747611:0.792581:0.742658:0.792581:0.000000
 :@0.404245:0.825903:0.408387:0.825903:0.408387:0.809405:0.404245:0.809405:0.000000
 :@0.404245:0.843254:0.408387:0.843254:0.408387:0.826756:0.404245:0.826756:0.000000
y por las propiedades i) y ii), resulta que::@0.427980:0.843254:0.711559:0.843254:0.711559:0.826756:0.427980:0.826756:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
  :@0.404245:0.869511:0.412529:0.869511:0.412529:0.853013:0.404245:0.853013:0.000000:0.000000
(  + 1)  =     [(  + 1)  –  ] =     (3  + 3  + 1):@0.508239:0.869511:0.811515:0.869515:0.811515:0.853017:0.508239:0.853013:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
n:@0.514192:0.869627:0.523555:0.869627:0.523555:0.853158:0.514192:0.853158:0.000000
3:@0.557093:0.863162:0.562047:0.863162:0.562047:0.853544:0.557093:0.853544:0.000000
j:@0.610671:0.869630:0.614524:0.869630:0.614524:0.853162:0.610671:0.853162:0.000000
3:@0.648064:0.863162:0.653017:0.863162:0.653017:0.853544:0.648064:0.853544:0.000000
j:@0.671800:0.869630:0.675653:0.869630:0.675653:0.853162:0.671800:0.853162:0.000000
3:@0.675653:0.863162:0.680607:0.863162:0.680607:0.853544:0.675653:0.853544:0.000000
j:@0.737725:0.869630:0.741578:0.869630:0.741578:0.853162:0.737725:0.853162:0.000000
2:@0.741579:0.863162:0.746532:0.863162:0.746532:0.853544:0.741579:0.853544:0.000000
j:@0.774121:0.869630:0.777974:0.869630:0.777974:0.853162:0.774121:0.853162:0.000000
 :@0.404228:0.911345:0.408370:0.911345:0.408370:0.894847:0.404228:0.894847:0.000000
= 3      + 3       +    1 = 3      +      (  + 1) +  ,:@0.500920:0.911345:0.818815:0.911344:0.818815:0.894846:0.500920:0.894847:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
j:@0.542861:0.911460:0.546714:0.911460:0.546714:0.894991:0.542861:0.894991:0.000000
2:@0.546730:0.904991:0.551684:0.904991:0.551684:0.895373:0.546730:0.895373:0.000000
j:@0.598826:0.911460:0.602679:0.911460:0.602679:0.894991:0.598826:0.894991:0.000000
j:@0.688776:0.911460:0.692629:0.911460:0.692629:0.894991:0.688776:0.894991:0.000000
2:@0.692625:0.904991:0.697579:0.904991:0.697579:0.895373:0.692625:0.895373:0.000000
n n:@0.732468:0.911460:0.756377:0.911460:0.756377:0.894991:0.732468:0.894991:0.000000:0.000000:0.000000
n:@0.807083:0.911460:0.816446:0.911460:0.816446:0.894991:0.807083:0.894991:0.000000
∑:@0.431052:0.219987:0.446430:0.219987:0.446430:0.194165:0.431052:0.194165:0.000000
n:@0.436486:0.200620:0.441945:0.200620:0.441945:0.191019:0.436486:0.191019:0.000000
j:@0.432465:0.225682:0.434712:0.225682:0.434712:0.216080:0.432465:0.216080:0.000000
=1:@0.434712:0.225614:0.445966:0.225614:0.445966:0.215996:0.434712:0.215996:0.000000:0.000000
∑:@0.431052:0.261964:0.446430:0.261964:0.446430:0.236141:0.431052:0.236141:0.000000
n:@0.436486:0.242597:0.441945:0.242597:0.441945:0.232995:0.436486:0.232995:0.000000
j:@0.432465:0.267658:0.434712:0.267658:0.434712:0.258056:0.432465:0.258056:0.000000
=1:@0.434712:0.267590:0.445966:0.267590:0.445966:0.257972:0.434712:0.257972:0.000000:0.000000
∑:@0.678987:0.219987:0.694366:0.219987:0.694366:0.194165:0.678987:0.194165:0.000000
n:@0.684422:0.200620:0.689880:0.200620:0.689880:0.191019:0.684422:0.191019:0.000000
j:@0.680401:0.225682:0.682647:0.225682:0.682647:0.216080:0.680401:0.216080:0.000000
=1:@0.682647:0.225614:0.693901:0.225614:0.693901:0.215996:0.682647:0.215996:0.000000:0.000000
∑:@0.761074:0.219987:0.776453:0.219987:0.776453:0.194165:0.761074:0.194165:0.000000
n:@0.766508:0.200620:0.771967:0.200620:0.771967:0.191019:0.766508:0.191019:0.000000
j:@0.762488:0.225682:0.764734:0.225682:0.764734:0.216080:0.762488:0.216080:0.000000
=1:@0.764734:0.225614:0.775988:0.225614:0.775988:0.215996:0.764734:0.215996:0.000000:0.000000
∑ ∑:@0.521515:0.219987:0.582125:0.219987:0.582125:0.194165:0.521515:0.194165:0.000000:0.000000:0.000000
n:@0.526949:0.200620:0.532408:0.200620:0.532408:0.191019:0.526949:0.191019:0.000000
j:@0.522928:0.225682:0.525175:0.225682:0.525175:0.216080:0.522928:0.216080:0.000000
=1:@0.525175:0.225614:0.536429:0.225614:0.536429:0.215996:0.525175:0.215996:0.000000:0.000000
n:@0.572181:0.200620:0.577639:0.200620:0.577639:0.191019:0.572181:0.191019:0.000000
j:@0.568160:0.225682:0.570406:0.225682:0.570406:0.216080:0.568160:0.216080:0.000000
=1:@0.570406:0.225614:0.581660:0.225614:0.581660:0.215996:0.570406:0.215996:0.000000:0.000000
∑:@0.622058:0.335839:0.637436:0.335839:0.637436:0.310016:0.622058:0.310016:0.000000
n:@0.627492:0.316472:0.632951:0.316472:0.632951:0.306871:0.627492:0.306871:0.000000
j:@0.623471:0.341533:0.625717:0.341533:0.625717:0.331932:0.623471:0.331932:0.000000
=1:@0.625717:0.341465:0.636972:0.341465:0.636972:0.331847:0.625717:0.331847:0.000000:0.000000
∑:@0.589658:0.396318:0.605037:0.396318:0.605037:0.370495:0.589658:0.370495:0.000000
n:@0.595095:0.376952:0.600553:0.376952:0.600553:0.367351:0.595095:0.367351:0.000000
j:@0.591074:0.402013:0.593320:0.402013:0.593320:0.392412:0.591074:0.392412:0.000000
=0:@0.593320:0.401945:0.604574:0.401945:0.604574:0.392327:0.593320:0.392327:0.000000:0.000000
∑:@0.764292:0.335839:0.779671:0.335839:0.779671:0.310016:0.764292:0.310016:0.000000
n:@0.769728:0.316472:0.775187:0.316472:0.775187:0.306871:0.769728:0.306871:0.000000
j:@0.765707:0.341533:0.767954:0.341533:0.767954:0.331932:0.765707:0.331932:0.000000
=1:@0.767954:0.341465:0.779208:0.341465:0.779208:0.331847:0.767954:0.331847:0.000000:0.000000
∑:@0.569991:0.490010:0.585370:0.490010:0.585370:0.464188:0.569991:0.464188:0.000000
n:@0.575426:0.470643:0.580884:0.470643:0.580884:0.461042:0.575426:0.461042:0.000000
j:@0.571405:0.495704:0.573651:0.495704:0.573651:0.486103:0.571405:0.486103:0.000000
=0:@0.573651:0.495637:0.584905:0.495637:0.584905:0.486019:0.573651:0.486019:0.000000:0.000000
∑:@0.568984:0.811146:0.584363:0.811146:0.584363:0.785324:0.568984:0.785324:0.000000
n:@0.574419:0.791779:0.579877:0.791779:0.579877:0.782178:0.574419:0.782178:0.000000
j:@0.570398:0.816841:0.572644:0.816841:0.572644:0.807239:0.570398:0.807239:0.000000
=0:@0.572644:0.816773:0.583898:0.816773:0.583898:0.807155:0.572644:0.807155:0.000000:0.000000
∑:@0.580557:0.872368:0.595936:0.872368:0.595936:0.846546:0.580557:0.846546:0.000000
n:@0.585993:0.853001:0.591452:0.853001:0.591452:0.843400:0.585993:0.843400:0.000000
j:@0.581972:0.878062:0.584218:0.878062:0.584218:0.868461:0.581972:0.868461:0.000000
=0:@0.584218:0.877995:0.595472:0.877995:0.595472:0.868377:0.584218:0.868377:0.000000:0.000000
∑:@0.705211:0.872368:0.720590:0.872368:0.720590:0.846546:0.705211:0.846546:0.000000
n:@0.710646:0.853001:0.716104:0.853001:0.716104:0.843400:0.710646:0.843400:0.000000
j:@0.706625:0.878062:0.708871:0.878062:0.708871:0.868461:0.706625:0.868461:0.000000
=0:@0.708871:0.877995:0.720125:0.877995:0.720125:0.868377:0.708871:0.868377:0.000000:0.000000
∑:@0.501333:0.549896:0.516712:0.549896:0.516712:0.524073:0.501333:0.524073:0.000000
n:@0.506768:0.530529:0.512226:0.530529:0.512226:0.520927:0.506768:0.520927:0.000000
j:@0.502747:0.555590:0.504993:0.555590:0.504993:0.545988:0.502747:0.545988:0.000000
=0:@0.504993:0.555522:0.516247:0.555522:0.516247:0.545904:0.504993:0.545904:0.000000:0.000000
∑:@0.625301:0.549896:0.640680:0.549896:0.640680:0.524073:0.625301:0.524073:0.000000
n:@0.630735:0.530529:0.636194:0.530529:0.636194:0.520927:0.630735:0.520927:0.000000
j:@0.626714:0.555590:0.628961:0.555590:0.628961:0.545988:0.626714:0.545988:0.000000
=0:@0.628961:0.555522:0.640215:0.555522:0.640215:0.545904:0.628961:0.545904:0.000000:0.000000
∑ ∑:@0.717439:0.549896:0.771348:0.549896:0.771348:0.524073:0.717439:0.524073:0.000000:0.000000:0.000000
n:@0.722873:0.530529:0.728332:0.530529:0.728332:0.520927:0.722873:0.520927:0.000000
j:@0.718853:0.555590:0.721099:0.555590:0.721099:0.545988:0.718853:0.545988:0.000000
=0:@0.721099:0.555522:0.732353:0.555522:0.732353:0.545904:0.721099:0.545904:0.000000:0.000000
n:@0.761404:0.530529:0.766863:0.530529:0.766863:0.520927:0.761404:0.520927:0.000000
j:@0.757383:0.555590:0.759629:0.555590:0.759629:0.545988:0.757383:0.545988:0.000000
=0:@0.759629:0.555522:0.770883:0.555522:0.770883:0.545904:0.759629:0.545904:0.000000:0.000000
∑:@0.806227:0.549896:0.821605:0.549896:0.821605:0.524073:0.806227:0.524073:0.000000
n:@0.811661:0.530529:0.817120:0.530529:0.817120:0.520927:0.811661:0.520927:0.000000
j:@0.807640:0.555590:0.809887:0.555590:0.809887:0.545988:0.807640:0.545988:0.000000
=0:@0.809887:0.555522:0.821141:0.555522:0.821141:0.545904:0.809887:0.545904:0.000000:0.000000
∑:@0.558053:0.604435:0.573432:0.604435:0.573432:0.578612:0.558053:0.578612:0.000000
n:@0.563488:0.585068:0.568946:0.585068:0.568946:0.575467:0.563488:0.575467:0.000000
j:@0.559467:0.610129:0.561713:0.610129:0.561713:0.600528:0.559467:0.600528:0.000000
=0:@0.561713:0.610061:0.572967:0.610061:0.572967:0.600443:0.561713:0.600443:0.000000:0.000000
∑:@0.576806:0.717007:0.592185:0.717007:0.592185:0.691185:0.576806:0.691185:0.000000
n:@0.582240:0.697640:0.587699:0.697640:0.587699:0.688039:0.582240:0.688039:0.000000
j:@0.578220:0.722701:0.580466:0.722701:0.580466:0.713100:0.578220:0.713100:0.000000
=0:@0.580466:0.722634:0.591720:0.722634:0.591720:0.713016:0.580466:0.713016:0.000000:0.000000
∑:@0.561972:0.639620:0.577350:0.639620:0.577350:0.613798:0.561972:0.613798:0.000000
n:@0.567406:0.620253:0.572865:0.620253:0.572865:0.610652:0.567406:0.610652:0.000000
j:@0.563386:0.645316:0.565632:0.645316:0.565632:0.635715:0.563386:0.635715:0.000000
=0:@0.565632:0.645249:0.576886:0.645249:0.576886:0.635631:0.565632:0.635631:0.000000:0.000000
n n:@0.725706:0.628988:0.749614:0.628988:0.749614:0.612519:0.725706:0.612519:0.000000:0.000000:0.000000
(  + 1):@0.734684:0.628872:0.779110:0.628872:0.779110:0.612375:0.734684:0.612375:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.748150:0.645211:0.756646:0.645211:0.756646:0.628713:0.748150:0.628713:0.000000
∑:@0.525269:0.914355:0.540648:0.914355:0.540648:0.888532:0.525269:0.888532:0.000000
n:@0.530705:0.894987:0.536164:0.894987:0.536164:0.885386:0.530705:0.885386:0.000000
j:@0.526684:0.920049:0.528930:0.920049:0.528930:0.910447:0.526684:0.910447:0.000000
=0:@0.528930:0.919981:0.540185:0.919981:0.540185:0.910363:0.528930:0.910363:0.000000:0.000000
∑ ∑:@0.580078:0.914355:0.634461:0.914355:0.634461:0.888532:0.580078:0.888532:0.000000:0.000000:0.000000
n:@0.585512:0.894987:0.590971:0.894987:0.590971:0.885386:0.585512:0.885386:0.000000
j:@0.581491:0.920049:0.583738:0.920049:0.583738:0.910447:0.581491:0.910447:0.000000
=0:@0.583738:0.919981:0.594992:0.919981:0.594992:0.910363:0.583738:0.910363:0.000000:0.000000
∑:@0.671740:0.914355:0.687119:0.914355:0.687119:0.888532:0.671740:0.888532:0.000000
n:@0.677176:0.894987:0.682635:0.894987:0.682635:0.885386:0.677176:0.885386:0.000000
j:@0.673155:0.920049:0.675402:0.920049:0.675402:0.910447:0.673155:0.910447:0.000000
=0:@0.675402:0.919981:0.686656:0.919981:0.686656:0.910363:0.675402:0.910363:0.000000:0.000000
n:@0.624518:0.894987:0.629977:0.894987:0.629977:0.885386:0.624518:0.885386:0.000000
j:@0.620498:0.920049:0.622744:0.920049:0.622744:0.910447:0.620498:0.910447:0.000000
=0:@0.622744:0.919981:0.633998:0.919981:0.633998:0.910363:0.622744:0.910363:0.000000:0.000000
3:@0.718079:0.903957:0.726575:0.903957:0.726575:0.887460:0.718079:0.887460:0.000000
2:@0.718079:0.920296:0.726575:0.920296:0.726575:0.903798:0.718079:0.903798:0.000000