1/2+3/2^2+5/2^3+7/2^4+…+2n-1/2^n
问题描述：
1/2+3/2^2+5/2^3+7/2^4+…+2n-1/2^n
答
设s=1/2+3/2^2+5/2^3+7/2^4+…+2n-1/2^n
1/2s= 1/2^2+3/2^3+5/2^4+…+2n-3/2^n+2n-1/2^(n+1)
s-1/2s=1/2+2/2^2+2/2^3+2/2^4+…+2/2^n—2n-1/2^(n+1)
1/2s= 1/2+（1/2+1/2^2+1/2^3+…+1/2^n-1）—2n-1/2^(n+1)
=1/2+（1-1/2^n-1）—2n-1/2^(n+1)
s=2（1/2s）=3+7-2n/2^n