1/6+1/12+1/20+...+1/(n^2+n)等于?
问题描述：
1/6+1/12+1/20+...+1/(n^2+n)等于?
答
1/(n^2+n)=1/n(n+1)=1/n-1/(n+1)
所以
1/6+1/12+1/20+...+1/(n^2+n）
=1/2-1/3+1/3-1/4+1/4-1/5+.+1/n-1/(n+1)
=1/2-1/(n+1)
=(n-1)/(2n+2)