Sn=(n-1)×2^(n+1)+2 证明如下：证：Sn=1×2+2×2^2+3×2^3+...+n×2^nSn/2=1+2×2+3×2^2+...+n×2^(n-1)Sn/2-Sn=-Sn/2=1+2+2^2+...+2^(n-1)-n×2^n=(2^n-1)/(2-1)-n×2^n=2^n-1-n×2^nSn=(n-1)×2^(n+1)+2