设第n项为an
an=n+ (2ⁿ-1)/2ⁿ=n+1 -1/2ⁿ
Sn=a1+a2+...+an
=(1+2+...+n)+n -(1/2+1/2²+...+1/2ⁿ)
=n(n+1)/2 +n -(1/2)(1-1/2ⁿ)/(1-1/2)
=n(n+3)/2 + 1/2ⁿ -1