Question

计算数列:1,2x,3x^2...nx^(n－1) x不为1的前n项和

Answer 1

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]