数列an=n*2^n-1用成公比错位相减求前n项和.
问题描述：
数列an=n*2^n-1用成公比错位相减求前n项和.
答
letS = 1.2^0+2.2^1+...+n.2^(n-1) (1)2S = 1.2^1+2.2^2+...+n.2^n (2)(2)-(1)S = n.2^n - ( 1+2+...+2^(n-1))= n.2^n - (2^n-1)= 1+ (n-1).2^na1+a2+...+an = S = 1+ (n-1).2^n