1/6+1/12+1/20+...+1/(n^2+n)等于?

来源：学生作业学帮网编辑：学帮网时间：2024/05/27 23:00:14

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)

原式=(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)

=1/2-1/3+1/3-1/4+...1/n-1/(n+1)
=1/2-1/(n+1)
=(n-1)/2(n+1)