求数列3x,5x^2,7x^3,...,(2n+1)x^n,...的前n项和

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求数列3x,5x^2,7x^3,...,(2n+1)x^n,...的前n项和

求数列3x,5x^2,7x^3,...,(2n+1)x^n,...的前n项和
求数列3x,5x^2,7x^3,...,(2n+1)x^n,...的前n项和

求数列3x,5x^2,7x^3,...,(2n+1)x^n,...的前n项和
Sn=3x+5x^2+7x^3+...+(2n+1)x^n
xSn=3x^2+5x^3+7x^4+...+(2n+1)x^(n+1)
(1-x)Sn=3x+2(x^2+x^3+...+x^n)-(2n+1)x^(n+1)
剩下的应该会了吧

x*S=3x^2+5x^3……
(1-X)S=3X+2(X^2+X^3……)-(2N+1)x^(N+1)
S=(3X+(1-2N)X^(N+1))/(1-X)

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