Question

已知数列｛an｝中,an=n+1/2的n次方,求其前n项和Sn

Answer 1

an=n+1/2^(n+1),

则

Sn=a1+a2+.+an

=(1+2+.+n)+(1/2^2+1/2^3+.+1/2^(n+1)) （分别是等差数列和等比数列）

=(n+1)n/2+1/2^2(1-1/2^n)/(1-1/2)

=(n+1)n/2+1/2-1/2^(n+1).