题目

1/1x2+1/2x3+1/3x4+...+1/nx(n+1)=_____

提问时间：2021-03-14

答案

裂项相消法.
1/(1*2)+1/(2*3)+1/(3*4)+.+1/[n(n+1)]
=(1-1/2)+(1/2-1/3)+(1/3-1/4)+.+[1/n-1/(n+1)]
=1-1/(n+1)
=n/(n+1)
填：n/(n+1)