数列an满足an=1/n^2+2n,求Sn
问题描述：
数列an满足an=1/n^2+2n,求Sn
答
可以采用裂项相消法.
因为 an=1/(n^2+2n)=1/[n(n+2)]=1/2*[1/n-1/(n+2)] ,
所以 Sn=1/2*[1-1/3+1/2-1/4+1/3-1/5+.+1/(n-1)-1/(n+1)+1/n-1/(n+2)]
=1/2*[1+1/2-1/(n+1)-1/(n+2)]
=(3n^2+5n)/[4(n+1)(n+2)] .