an=2n/2^n 求sn
问题描述：
an=2n/2^n 求sn
答
an=2n/2^n
Sn=2(1/2^1+2/2^2+3/2^3+...+n/2^n)
Sn/2=2[1/2^2+2/2^3+...+(n-1)/2^n+n/2^(n+1)]
Sn-Sn/2=Sn/2=2[1/2^1+1/2^2+1/2^3+...+1/2^n-n/2^(n+1)]
=2[(1/2)(1-1/2^n)/(1-1/2)-2n/2^n]
=2(1-1/2^n-2n/2^n)
=2[1-(2n+1)/2^n]
Sn=4[1-(2n+1)/2^n]
=4-(2n+1)/2^(n-2)