113:@0.916858:0.966074:0.945034:0.966074:0.945034:0.949450:0.916858:0.949450:0.000000:0.000000:0.000000
Teorema del binomio:@0.095800:0.136304:0.316473:0.136304:0.316473:0.114495:0.095800:0.114495:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Para determinar esta fórmula, encontraremos por multiplicación directa los :@0.095800:0.257075:0.698200:0.257075:0.698200:0.241406:0.095800:0.241406:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
desarrollos de los binomios hasta la quinta potencia.:@0.095800:0.273672:0.479237:0.273672:0.479237:0.258002:0.095800:0.258002:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.390937:0.463465:0.394973:0.463465:0.394973:0.447795:0.390937:0.447795:0.000000
El análisis del desarrollo de estos binomios nos permite encontrar la fórmula que :@0.095800:0.483630:0.698261:0.483630:0.698261:0.467960:0.095800:0.467960:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
aplicaremos::@0.095800:0.500226:0.187828:0.500226:0.187828:0.484556:0.095800:0.484556:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1. :@0.124289:0.523945:0.143031:0.523945:0.143031:0.506809:0.124289:0.506809:0.000000:0.000000:0.000000
Si el exponente del binomio es  , hay :@0.152779:0.523945:0.430429:0.523945:0.430429:0.508275:0.152779:0.508275:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
n:@0.383401:0.523945:0.392910:0.523945:0.392910:0.507584:0.383401:0.507584:0.000000
n+1:@0.430429:0.523945:0.459434:0.523945:0.459434:0.507584:0.430429:0.507584:0.000000:0.000000:0.000000
 términos en el desarrollo.:@0.459434:0.523945:0.648112:0.523945:0.648112:0.508275:0.459434:0.508275:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2. :@0.124290:0.547664:0.143031:0.547664:0.143031:0.530528:0.124290:0.530528:0.000000:0.000000:0.000000
Para cada valor de  , el desarrollo de :@0.152779:0.547664:0.421362:0.547664:0.421362:0.531994:0.152779:0.531994:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
n:@0.288831:0.547664:0.298339:0.547664:0.298339:0.531303:0.288831:0.531303:0.000000
(a + b):@0.421178:0.547664:0.466805:0.547664:0.466805:0.531303:0.421178:0.531303:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
n:@0.466845:0.541626:0.472388:0.541626:0.472388:0.532087:0.466845:0.532087:0.000000
 empieza con  y termina con :@0.472388:0.547673:0.698165:0.547673:0.698165:0.532003:0.472388:0.532003:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.574625:0.547673:0.583894:0.547673:0.583894:0.531312:0.574625:0.531312:0.000000
n  :@0.583907:0.541626:0.593233:0.541626:0.593233:0.532087:0.583907:0.532087:0.000000:0.000000:0.000000
b:@0.152781:0.564269:0.162050:0.564269:0.162050:0.547908:0.152781:0.547908:0.000000
n:@0.162053:0.558222:0.167597:0.558222:0.167597:0.548683:0.162053:0.548683:0.000000
. En cada término los exponentes de   y   suman  .:@0.167597:0.564269:0.543148:0.564269:0.543148:0.548599:0.167597:0.548599:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a b:@0.437650:0.564269:0.472368:0.564269:0.472368:0.547908:0.437650:0.547908:0.000000:0.000000:0.000000
n:@0.530433:0.564269:0.539942:0.564269:0.539942:0.547908:0.530433:0.547908:0.000000
3. :@0.124292:0.587988:0.143033:0.587988:0.143033:0.570852:0.124292:0.570852:0.000000:0.000000:0.000000
Las potencias de   disminuyen de 1 en 1 al pasar de cada término al :@0.152781:0.587988:0.698129:0.587988:0.698129:0.572318:0.152781:0.572318:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.288261:0.587988:0.297530:0.587988:0.297530:0.571627:0.288261:0.571627:0.000000
siguiente. La   aparece por primera vez en el segundo término con :@0.152781:0.604584:0.698141:0.604584:0.698141:0.588915:0.152781:0.588915:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
b:@0.257503:0.604584:0.266773:0.604584:0.266773:0.588223:0.257503:0.588223:0.000000
exponente 1 que aumenta de 1 en 1. El exponente de   siempre es una :@0.152781:0.621181:0.698145:0.621181:0.698145:0.605511:0.152781:0.605511:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
b:@0.565870:0.621181:0.575139:0.621181:0.575139:0.604820:0.565870:0.604820:0.000000
unidad menor que el número de orden del término.:@0.152781:0.637777:0.533712:0.637777:0.533712:0.622108:0.152781:0.622108:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
4. :@0.124292:0.661496:0.143033:0.661496:0.143033:0.644360:0.124292:0.644360:0.000000:0.000000:0.000000
El primer coeficiente es la unidad. El de cualquier otro término se obtiene :@0.152781:0.661496:0.698234:0.661496:0.698234:0.645826:0.152781:0.645826:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
multiplicando en el término anterior su coeficiente por el exponente de   :@0.152781:0.678093:0.698237:0.678093:0.698237:0.662423:0.152781:0.662423:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.684932:0.678093:0.694202:0.678093:0.694202:0.661731:0.684932:0.661731:0.000000
y dividiendo ese producto entre el número de términos anteriores al que :@0.152781:0.694689:0.698182:0.694689:0.698182:0.679019:0.152781:0.679019:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
se trata de formar.:@0.152781:0.711285:0.284408:0.711285:0.284408:0.695616:0.152781:0.695616:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Ejemplo 2:@0.095800:0.753357:0.165306:0.753357:0.165306:0.738244:0.095800:0.738244:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Desarrollar ( + 2 7.:@0.095800:0.777395:0.238502:0.777395:0.238502:0.761726:0.095800:0.761726:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x :@0.183145:0.777395:0.193926:0.777395:0.193926:0.761034:0.183145:0.761034:0.000000:0.000000
y):@0.217937:0.777395:0.230302:0.777395:0.230302:0.761034:0.217937:0.761034:0.000000:0.000000
Solución:@0.095800:0.799298:0.156461:0.799298:0.156461:0.784185:0.095800:0.784185:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
El desarrollo tendrá 8 términos, iniciará con  7 y terminará con 128 7. :@0.095800:0.823336:0.597419:0.823336:0.597419:0.807666:0.095800:0.807666:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x :@0.414484:0.823336:0.424343:0.823336:0.424343:0.806975:0.414484:0.806975:0.000000:0.000000
y :@0.577700:0.823336:0.587392:0.823336:0.587392:0.806975:0.577700:0.806975:0.000000:0.000000
Para obtener los coeficientes, tomamos en cuenta la conclusión 4.:@0.095800:0.847055:0.578472:0.847055:0.578472:0.831385:0.095800:0.831385:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
+:@0.118521:0.888900:0.056862:0.888900:0.056862:0.873328:0.118521:0.873328:0.000000
+:@0.190296:0.888900:0.128637:0.888900:0.128637:0.873328:0.190296:0.873328:0.000000
+:@0.274842:0.888900:0.197262:0.888900:0.197262:0.873328:0.274842:0.873328:0.000000
+:@0.362539:0.888900:0.284959:0.888900:0.284959:0.873328:0.362539:0.873328:0.000000
+:@0.450237:0.888900:0.372656:0.888900:0.372656:0.873328:0.450237:0.873328:0.000000
+:@0.534766:0.888900:0.473107:0.888900:0.473107:0.873328:0.534766:0.873328:0.000000
+:@0.606541:0.888900:0.544883:0.888900:0.544883:0.873328:0.606541:0.873328:0.000000
x:@0.099884:0.888223:0.107347:0.888223:0.107347:0.871862:0.099884:0.871862:0.000000
x:@0.141604:0.888223:0.149067:0.888223:0.149067:0.871862:0.141604:0.871862:0.000000
y:@0.173649:0.888223:0.181131:0.888223:0.181131:0.871862:0.173649:0.871862:0.000000
x:@0.219516:0.888223:0.226979:0.888223:0.226979:0.871862:0.219516:0.871862:0.000000
y:@0.250917:0.888223:0.258398:0.888223:0.258398:0.871862:0.250917:0.871862:0.000000
x:@0.306365:0.888223:0.313829:0.888223:0.313829:0.871862:0.306365:0.871862:0.000000
y:@0.338816:0.888223:0.346298:0.888223:0.346298:0.871862:0.338816:0.871862:0.000000
x:@0.394044:0.888223:0.401507:0.888223:0.401507:0.871862:0.394044:0.871862:0.000000
y:@0.425463:0.888223:0.432945:0.888223:0.432945:0.871862:0.425463:0.871862:0.000000
x:@0.479438:0.888223:0.486901:0.888223:0.486901:0.871862:0.479438:0.871862:0.000000
y:@0.511060:0.888223:0.518541:0.888223:0.518541:0.871862:0.511060:0.871862:0.000000
x y:@0.557866:0.888223:0.589677:0.888223:0.589677:0.871862:0.557866:0.871862:0.000000:0.000000:0.000000
y:@0.634972:0.888223:0.642454:0.888223:0.642454:0.871862:0.634972:0.871862:0.000000
7(2) 21 (2 ):@0.130981:0.888223:0.265337:0.888223:0.265337:0.872553:0.130981:0.872553:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
35(2):@0.287727:0.888223:0.353237:0.888223:0.353237:0.872553:0.287727:0.872553:0.000000:0.000000:0.000000:0.000000:0.000000
35 (2 ):@0.375424:0.888223:0.439884:0.888223:0.439884:0.872553:0.375424:0.872553:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
21(2):@0.463121:0.888223:0.525480:0.888223:0.525480:0.872553:0.463121:0.872553:0.000000:0.000000:0.000000:0.000000:0.000000
7(2):@0.547243:0.888223:0.596629:0.888223:0.596629:0.872553:0.547243:0.872553:0.000000:0.000000:0.000000:0.000000
(2 ):@0.619019:0.888223:0.649406:0.888223:0.649406:0.872553:0.619019:0.872553:0.000000:0.000000:0.000000:0.000000
7:@0.108783:0.880561:0.113995:0.880561:0.113995:0.871479:0.108783:0.871479:0.000000
6:@0.150925:0.880561:0.156137:0.880561:0.156137:0.871479:0.150925:0.871479:0.000000
5:@0.228620:0.880561:0.233831:0.880561:0.233831:0.871479:0.228620:0.871479:0.000000
2:@0.265315:0.880561:0.270527:0.880561:0.270527:0.871479:0.265315:0.871479:0.000000
4:@0.315894:0.880561:0.321106:0.880561:0.321106:0.871479:0.315894:0.871479:0.000000
3:@0.353219:0.880561:0.358431:0.880561:0.358431:0.871479:0.353219:0.871479:0.000000
3:@0.403168:0.880561:0.408380:0.880561:0.408380:0.871479:0.403168:0.871479:0.000000
4:@0.440291:0.880561:0.445502:0.880561:0.445502:0.871479:0.440291:0.871479:0.000000
2:@0.488552:0.880561:0.493764:0.880561:0.493764:0.871479:0.488552:0.871479:0.000000
5:@0.525461:0.880561:0.530672:0.880561:0.530672:0.871479:0.525461:0.871479:0.000000
6:@0.596802:0.880561:0.602013:0.880561:0.602013:0.871479:0.596802:0.871479:0.000000
7:@0.649153:0.880561:0.654365:0.880561:0.654365:0.871479:0.649153:0.871479:0.000000
 :@0.658682:0.894509:0.662717:0.894509:0.662717:0.878840:0.658682:0.878840:0.000000
+:@0.118521:0.920169:0.069264:0.920169:0.069264:0.904596:0.118521:0.904596:0.000000
+:@0.177895:0.920169:0.128637:0.920169:0.128637:0.904596:0.177895:0.904596:0.000000
+:@0.245045:0.920169:0.178724:0.920169:0.178724:0.904596:0.245045:0.904596:0.000000
+:@0.321483:0.920169:0.255162:0.920169:0.255162:0.904596:0.321483:0.904596:0.000000
+:@0.397921:0.920169:0.331599:0.920169:0.331599:0.904596:0.397921:0.904596:0.000000
+:@0.473514:0.920169:0.415467:0.920169:0.415467:0.904596:0.473514:0.904596:0.000000
+:@0.541678:0.920169:0.483631:0.920169:0.483631:0.904596:0.541678:0.904596:0.000000
x:@0.099884:0.919491:0.107347:0.919491:0.107347:0.903130:0.099884:0.903130:0.000000
x y:@0.150044:0.919491:0.174000:0.919491:0.174000:0.903130:0.150044:0.903130:0.000000:0.000000:0.000000
x y:@0.210542:0.919491:0.233889:0.919491:0.233889:0.903130:0.210542:0.903130:0.000000:0.000000:0.000000
x y:@0.286150:0.919491:0.310530:0.919491:0.310530:0.903130:0.286150:0.903130:0.000000:0.000000:0.000000
x y:@0.362570:0.919491:0.385917:0.919491:0.385917:0.903130:0.362570:0.903130:0.000000:0.000000:0.000000
x y:@0.439007:0.919491:0.462558:0.919491:0.462558:0.903130:0.439007:0.903130:0.000000:0.000000:0.000000
xy:@0.515335:0.919491:0.530102:0.919491:0.530102:0.903130:0.515335:0.903130:0.000000:0.000000
y:@0.581626:0.919491:0.589107:0.919491:0.589107:0.903130:0.581626:0.903130:0.000000
14:@0.130247:0.919491:0.148030:0.919491:0.148030:0.903821:0.130247:0.903821:0.000000:0.000000
84:@0.190764:0.919491:0.208546:0.919491:0.208546:0.903821:0.190764:0.903821:0.000000:0.000000
280:@0.257932:0.919491:0.284505:0.919491:0.284505:0.903821:0.257932:0.903821:0.000000:0.000000:0.000000
560:@0.334370:0.919491:0.360943:0.919491:0.360943:0.903821:0.334370:0.903821:0.000000:0.000000:0.000000
672:@0.411177:0.919491:0.437749:0.919491:0.437749:0.903821:0.411177:0.903821:0.000000:0.000000:0.000000
448:@0.487135:0.919491:0.513708:0.919491:0.513708:0.903821:0.487135:0.903821:0.000000:0.000000:0.000000
128:@0.553420:0.919491:0.579992:0.919491:0.579992:0.903821:0.553420:0.903821:0.000000:0.000000:0.000000
7:@0.108783:0.911830:0.113995:0.911830:0.113995:0.902748:0.108783:0.902748:0.000000
6:@0.159351:0.911830:0.164563:0.911830:0.164563:0.902748:0.159351:0.902748:0.000000
52:@0.219659:0.911830:0.240730:0.911830:0.240730:0.902748:0.219659:0.902748:0.000000:0.000000
4:@0.295677:0.911830:0.300889:0.911830:0.300889:0.902748:0.295677:0.902748:0.000000
3:@0.312167:0.911830:0.317378:0.911830:0.317378:0.902748:0.312167:0.902748:0.000000
3:@0.371695:0.911830:0.376907:0.911830:0.376907:0.902748:0.371695:0.902748:0.000000
4:@0.387981:0.911830:0.393193:0.911830:0.393193:0.902748:0.387981:0.902748:0.000000
2:@0.448129:0.911830:0.453341:0.911830:0.453341:0.902748:0.448129:0.902748:0.000000
5:@0.464202:0.911830:0.469414:0.911830:0.469414:0.902748:0.464202:0.902748:0.000000
6:@0.531938:0.911830:0.537150:0.911830:0.537150:0.902748:0.531938:0.902748:0.000000
7:@0.590516:0.911830:0.595728:0.911830:0.595728:0.902748:0.590516:0.902748:0.000000
El teorema del binomio o de Newton es una fórmula con la cual se pueden :@0.106973:0.182311:0.685562:0.182311:0.685562:0.166641:0.106973:0.166641:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
escribir  directamente los términos del desarrollo de  una potencia entera :@0.106973:0.198908:0.685667:0.198908:0.685667:0.183238:0.106973:0.183238:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.681584:0.198908:0.685619:0.198908:0.685619:0.183238:0.681584:0.183238:0.000000
y positiva de un binomio :@0.106973:0.215504:0.293276:0.215504:0.293276:0.199834:0.106973:0.199834:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
(a + b):@0.293276:0.215504:0.339198:0.215504:0.339198:0.199143:0.293276:0.199143:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
n:@0.341222:0.209457:0.346766:0.209457:0.346766:0.199918:0.341222:0.199918:0.000000
.:@0.347946:0.215504:0.351153:0.215504:0.351153:0.199834:0.347946:0.199834:0.000000
En los coeficientes :@0.733044:0.164757:0.859690:0.164757:0.859690:0.150512:0.733044:0.150512:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
de los términos del :@0.733044:0.179844:0.864079:0.179844:0.864079:0.165599:0.733044:0.165599:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
desarrollo de los :@0.733044:0.194932:0.845838:0.194932:0.845838:0.180687:0.733044:0.180687:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
binomios, la simetría :@0.733044:0.210020:0.873896:0.210020:0.873896:0.195774:0.733044:0.195774:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
que se obtiene es :@0.733044:0.225107:0.854633:0.225107:0.854633:0.210862:0.733044:0.210862:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
similar a los números :@0.733044:0.240195:0.876744:0.240195:0.876744:0.225950:0.733044:0.225950:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
dispuestos en el :@0.733044:0.255282:0.844446:0.255282:0.844446:0.241037:0.733044:0.241037:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
triángulo de Pascal.:@0.733044:0.270370:0.861533:0.270370:0.861533:0.256125:0.733044:0.256125:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.733044:0.292587:0.736713:0.292587:0.736713:0.278341:0.733044:0.278341:0.000000
Si el binomio tiene :@0.733044:0.314803:0.861350:0.314803:0.861350:0.300558:0.733044:0.300558:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
signo negativo, :@0.733044:0.329891:0.838482:0.329891:0.838482:0.315645:0.733044:0.315645:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
en el desarrollo se :@0.733044:0.344978:0.856708:0.344978:0.856708:0.330733:0.733044:0.330733:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
colocan los signos :@0.733044:0.360066:0.858534:0.360066:0.858534:0.345821:0.733044:0.345821:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
alternadamente.:@0.733044:0.375153:0.842536:0.375153:0.842536:0.360908:0.733044:0.360908:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Recuerda que...:@0.763096:0.139731:0.885177:0.139731:0.885177:0.122831:0.763096:0.122831:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
(:@0.871739:0.395214:0.874597:0.395214:0.874597:0.385710:0.871739:0.385710:0.000000
):@0.892034:0.395214:0.894893:0.395214:0.894893:0.385710:0.892034:0.385710:0.000000
(:@0.871739:0.406837:0.874597:0.406837:0.874597:0.397333:0.871739:0.397333:0.000000
):@0.892034:0.406837:0.894893:0.406837:0.894893:0.397333:0.892034:0.397333:0.000000
(:@0.871739:0.418460:0.874597:0.418460:0.874597:0.408956:0.871739:0.408956:0.000000
):@0.892034:0.418460:0.894893:0.418460:0.894893:0.408956:0.892034:0.408956:0.000000
(:@0.871739:0.430083:0.874597:0.430083:0.874597:0.420579:0.871739:0.420579:0.000000
):@0.892034:0.430083:0.894893:0.430083:0.894893:0.420579:0.892034:0.420579:0.000000
(:@0.871739:0.441706:0.874597:0.441706:0.874597:0.432201:0.871739:0.432201:0.000000
):@0.892034:0.441706:0.894893:0.441706:0.894893:0.432201:0.892034:0.432201:0.000000
(:@0.871739:0.453329:0.874597:0.453329:0.874597:0.443824:0.871739:0.443824:0.000000
):@0.892034:0.453329:0.894893:0.453329:0.894893:0.443824:0.892034:0.443824:0.000000
(:@0.871739:0.464952:0.874597:0.464952:0.874597:0.455447:0.871739:0.455447:0.000000
):@0.892034:0.464952:0.894893:0.464952:0.894893:0.455447:0.892034:0.455447:0.000000
+:@0.880909:0.394343:0.885622:0.394343:0.885622:0.387088:0.880909:0.387088:0.000000
+:@0.880909:0.405966:0.885622:0.405966:0.885622:0.398711:0.880909:0.398711:0.000000
+:@0.880909:0.417590:0.885622:0.417590:0.885622:0.410335:0.880909:0.410335:0.000000
+:@0.880909:0.429214:0.885622:0.429214:0.885622:0.421959:0.880909:0.421959:0.000000
+:@0.880909:0.440838:0.885622:0.440838:0.885622:0.433582:0.880909:0.433582:0.000000
+:@0.880909:0.452461:0.885622:0.452461:0.885622:0.445206:0.880909:0.445206:0.000000
+:@0.880909:0.464085:0.885622:0.464085:0.885622:0.456830:0.880909:0.456830:0.000000
xy:@0.875617:0.394027:0.891079:0.394027:0.891079:0.386405:0.875617:0.386405:0.000000:0.000000
xy:@0.875617:0.405651:0.891079:0.405651:0.891079:0.398028:0.875617:0.398028:0.000000:0.000000
xy:@0.875617:0.417274:0.891079:0.417274:0.891079:0.409652:0.875617:0.409652:0.000000:0.000000
xy:@0.875617:0.428898:0.891079:0.428898:0.891079:0.421276:0.875617:0.421276:0.000000:0.000000
xy:@0.875617:0.440522:0.891079:0.440522:0.891079:0.432899:0.875617:0.432899:0.000000:0.000000
xy:@0.875617:0.452146:0.891079:0.452146:0.891079:0.444523:0.875617:0.444523:0.000000:0.000000
xy:@0.875617:0.463769:0.891079:0.463769:0.891079:0.456147:0.875617:0.456147:0.000000:0.000000
0:@0.894835:0.389633:0.897263:0.389633:0.897263:0.385402:0.894835:0.385402:0.000000
1:@0.894519:0.401257:0.896947:0.401257:0.896947:0.397026:0.894519:0.397026:0.000000
2:@0.894837:0.412881:0.897265:0.412881:0.897265:0.408651:0.894837:0.408651:0.000000
3:@0.894837:0.424506:0.897265:0.424506:0.897265:0.420275:0.894837:0.420275:0.000000
4:@0.895031:0.436130:0.897459:0.436130:0.897459:0.431900:0.895031:0.431900:0.000000
5:@0.894837:0.447755:0.897265:0.447755:0.897265:0.443524:0.894837:0.443524:0.000000
6:@0.894937:0.459379:0.897364:0.459379:0.897364:0.455149:0.894937:0.455149:0.000000
1:@0.787273:0.397386:0.793086:0.397386:0.793086:0.387257:0.787273:0.387257:0.000000
1 1:@0.778090:0.407496:0.801078:0.407496:0.801078:0.397368:0.778090:0.397368:0.000000:0.000000:0.000000
1:@0.768906:0.418509:0.774719:0.418509:0.774719:0.408381:0.768906:0.408381:0.000000
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1:@0.740439:0.453918:0.746252:0.453918:0.746252:0.443790:0.740439:0.443790:0.000000
1 6 15 20:@0.730315:0.466183:0.796040:0.466183:0.796040:0.456055:0.730315:0.456055:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
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5 10 10:@0.758913:0.453918:0.806890:0.453918:0.806890:0.443790:0.758913:0.443790:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
4 6:@0.771360:0.441904:0.793479:0.441904:0.793479:0.431776:0.771360:0.431776:0.000000:0.000000:0.000000
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4:@0.803258:0.441904:0.809070:0.441904:0.809070:0.431776:0.803258:0.431776:0.000000
5 1:@0.816371:0.453918:0.838752:0.453918:0.838752:0.443790:0.816371:0.443790:0.000000:0.000000:0.000000
6:@0.827901:0.466183:0.833714:0.466183:0.833714:0.456055:0.827901:0.456055:0.000000
15:@0.806164:0.466183:0.817789:0.466183:0.817789:0.456055:0.806164:0.456055:0.000000:0.000000
1:@0.821958:0.441904:0.827770:0.441904:0.827770:0.431776:0.821958:0.431776:0.000000
1:@0.813465:0.430533:0.819278:0.430533:0.819278:0.420405:0.813465:0.420405:0.000000
Amplía:@0.732737:0.742548:0.781554:0.742548:0.781554:0.727435:0.732737:0.727435:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.781386:0.742548:0.784854:0.742548:0.784854:0.727184:0.781386:0.727184:0.000000
tu conocimiento :@0.784686:0.742548:0.897311:0.742548:0.897311:0.728303:0.784686:0.728303:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
sobre el triángulo de :@0.732737:0.757636:0.874411:0.757636:0.874411:0.743391:0.732737:0.743391:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Pascal y binomio de :@0.732737:0.772723:0.869186:0.772723:0.869186:0.758478:0.732737:0.758478:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Newton. :@0.732737:0.787811:0.793262:0.787811:0.793262:0.773566:0.732737:0.773566:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Ingresa :@0.793262:0.787811:0.847959:0.787811:0.847959:0.772698:0.793262:0.772698:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
en el :@0.847959:0.787811:0.884077:0.787811:0.884077:0.773566:0.847959:0.773566:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
siguiente enlace web: :@0.732737:0.802899:0.881430:0.802899:0.881430:0.788653:0.732737:0.788653:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
lynk.ec/9m09:@0.732737:0.817986:0.822647:0.817986:0.822647:0.802861:0.732737:0.802861:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Competencia digital:@0.747928:0.716918:0.898593:0.716918:0.898593:0.700017:0.747928:0.700017:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
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):@0.262951:0.321649:0.269088:0.321649:0.269088:0.301248:0.262951:0.301248:0.000000
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):@0.262951:0.346597:0.269088:0.346597:0.269088:0.326196:0.262951:0.326196:0.000000
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):@0.262951:0.396493:0.269088:0.396493:0.269088:0.376092:0.262951:0.376092:0.000000
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):@0.262951:0.421441:0.269088:0.421441:0.269088:0.401040:0.262951:0.401040:0.000000
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=:@0.279228:0.319777:0.289345:0.319777:0.289345:0.304204:0.279228:0.304204:0.000000
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= +:@0.276777:0.344727:0.312748:0.344727:0.312748:0.329154:0.276777:0.329154:0.000000:0.000000:0.000000
+:@0.239811:0.369677:0.249928:0.369677:0.249928:0.354104:0.239811:0.354104:0.000000
=:@0.279025:0.369677:0.289142:0.369677:0.289142:0.354104:0.279025:0.354104:0.000000
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=:@0.278823:0.394627:0.288939:0.394627:0.288939:0.379054:0.278823:0.379054:0.000000
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+:@0.239793:0.419576:0.249910:0.419576:0.249910:0.404003:0.239793:0.404003:0.000000
=:@0.279836:0.419576:0.289953:0.419576:0.289953:0.404003:0.279836:0.404003:0.000000
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+:@0.473898:0.419576:0.484014:0.419576:0.484014:0.404003:0.473898:0.404003:0.000000
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=:@0.278804:0.444526:0.288921:0.444526:0.288921:0.428953:0.278804:0.428953:0.000000
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ab:@0.227686:0.319099:0.261925:0.319099:0.261925:0.302738:0.227686:0.302738:0.000000:0.000000
ab:@0.227686:0.344049:0.261925:0.344049:0.261925:0.327688:0.227686:0.327688:0.000000:0.000000
ab:@0.290506:0.344049:0.324744:0.344049:0.324744:0.327688:0.290506:0.327688:0.000000:0.000000
ab:@0.227686:0.368999:0.261925:0.368999:0.261925:0.352638:0.227686:0.352638:0.000000:0.000000
a:@0.292754:0.368999:0.302023:0.368999:0.302023:0.352638:0.292754:0.352638:0.000000
abb:@0.334161:0.368999:0.377613:0.368999:0.377613:0.352638:0.334161:0.352638:0.000000:0.000000:0.000000
ab:@0.227686:0.393949:0.261925:0.393949:0.261925:0.377588:0.227686:0.377588:0.000000:0.000000
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ab:@0.382386:0.393949:0.400869:0.393949:0.400869:0.377588:0.382386:0.377588:0.000000:0.000000
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ab:@0.227686:0.418899:0.261925:0.418899:0.261925:0.402537:0.227686:0.402537:0.000000:0.000000
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ab:@0.512319:0.443849:0.530836:0.443847:0.530836:0.427486:0.512319:0.427487:0.000000:0.000000
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4:@0.343612:0.436200:0.348824:0.436200:0.348824:0.427118:0.343612:0.427118:0.000000
32:@0.401507:0.436200:0.421851:0.436200:0.421851:0.427118:0.401507:0.427118:0.000000:0.000000
23:@0.466055:0.436200:0.486602:0.436200:0.486602:0.427118:0.466055:0.427118:0.000000:0.000000
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®EDUCACIÓN – Libro resuelto solo para fines didácticos – Prohibida su reproducción :@0.079553:0.684191:0.079553:0.268044:0.061505:0.268044:0.061505:0.684191:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000