an=（2^n-1）n,求Sn
问题描述：
an=（2^n-1）n,求Sn
答
an=（2^n-1)n=2^n*n-n,令
Tn=2^1*1+2^*2+…2^n*n,①则
2Tn=2^2*1+2^3*2+…+2^n*(n-1)+2^(n+1)*n ②
②-①得Tn=-(2^1+2^2+…+2^n)+2^(n+1)*n=2^(n+1)-2+2^(n+1)*n
Sn=Tn-(1+2+…+n)=(n+1)*2^(n+1)-2-n(n+1)/2