数列1/2,3/4,5/8,7/16...前n项和.
问题描述：
数列1/2,3/4,5/8,7/16...前n项和.
答
an=(2n-1)/2^n
sn= 1/2+3/4+ ..+(2n-1)/2^n
2sn=1+3/2 ...+(2n-1)/2^n-1
sn=2sn-sn=1+2(1/2+1/4+1/8+...+1/2^n-1)-(2n-1)/2^n
=1+2*(1/2-1/2^n)/(1-1/2)-(2n-1)/2^n
=1+2-4/2^n -(2n-1)/2^n
=3-(3+2n)/2^n