1/1*2+1/2*3+…+1/n(n+1)

问题描述:

1/1*2+1/2*3+…+1/n(n+1)

因为
1/n(n+1)=1/n-1/(n+1)
所以
1/1*2+1/2*3+…+1/n(n+1)
=1-1/2+1/2-1/3+...+1/n-1/(n+1)
=1-1/(n+1)
=n/(n+1)