计算数列:1,2x,3x^2...nx^(n－1) x不为1的前n项和

来源：学生作业帮编辑：作业帮分类：数学作业时间：2024/11/08 06:41:13

let
S = 1.x^0+2.x^1+...+n.x^(n-1) (1)
xS = 1.x^1+2.x^2+...+n.x^n (2)
(1)-(2)
(1-x)S = [1+x+x^2+...+x^(n-1)]-n.x^n
= (1-x^n)/(x-1) - nx^n
S = [1/(1-x)] [(1-x^n)/(x-1) - nx^n]

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