Sn=1/2+3*(1/4)+5*(1/8)....+(2n-1)*(1/2)^n
(1/2)Sn=1/4+3*(1/8)+....+(2n-1)*(1/2)^(n+1)
Sn-(1/2)Sn=1/2+2*(1/4)+2*(1/8)+...+2(1/2)^n-(2n-1)*(1/2)^(n+1)
=1/2+1/2+1/4+1/8+...+(1/2)^(n-1)-(2n-1)*(1/2)^(n+1)=(1/2)Sn
Sn=1+[1+1/2+1/4+...+(1/2)^(n-2)]-(2n-1)*(1/2)^(n+1)
等比数列求和就得结果了