数列an=n乘2的n次方,求sn
问题描述：
数列an=n乘2的n次方,求sn
如题,
答
S[n] = 1·2 + 2·2^2 + 3·2^3 + ...+ n·2^n2·S[n] = 1·2^2 + 2·2^3 + 3·2^4 + ...+ n·2^(n+1)两式相减-S[n] = S[n] - 2·S[n] = 1·2 + 2^2 + 2^3 + ...+ 2^n - n·2^(n+1)= 2^(n+1) - 2 - n·2^(n+1)= (1-n...