3/2=1+1/2
9/4=2+1/4
13/4=3+1/4
65/16=4+1/16
.
An=n+2^(-n)
Sn=(1+2+...+n)+(1/2+1/4+1/8+1/16+...+1/2^n)
=(1+n)*n/2+(1-2^(-n))