求数列2/2,4/2的平方,6/2的3次方,…,2n/2n次方前n项和Sn 传图片!

2/2,4/2^2,6/2^3,...,2n/2^n
let
S = 1.(1/2)^0+2.(1/2)^1+...+n.(1/2)^(n-1) (1)
(1/2)S = 1.(1/2)^1+2.(1/2)^2+...+n.(1/2)^n (2)
(1)-(2)
(1/2)S = [1+ 1/2+...+1/2^(n-1)] -n.(1/2)^n
= 2(1- (1/2)^n) -n.(1/2)^n
= 2 - (n+2)(1/2)^n
S = 4-2(n+2)(1/2)^n
an = 2n/2^n
= n(1/2)^(n-1)
Sn =b1+b2+...+bn
=S
=4-2(n+2)(1/2)^n