等比数列(n×2*n),q=2,求前n项和_其他解答

等比数列(n×2*n),q=2,求前n项和

人气：352 ℃　时间：2020-05-14 02:22:03

解答

let
S = 1.2^1+2.2^2+.+n.2^n (1)
2S = 1.2^2+2.2^3+.+n.2^(n+1) (2)
(2)-(1)
S = n.2^(n+1) - (2+2^2+...+2^n)
=n.2^(n+1) - 2(2^n -1)
= 2+ (2n-2).2^n