Question

一乘二分之一加二乘三分之一加三乘四分之一加省略号加n乘(N+1_)分之一

Answer 1

1/n(n+1)
=[(n+1)-n]/n(n+1)
=(n+1)/n(n+1)-n/n(n+1)
=1/n-1/(n+1)
所以原式=1-1/2+1/2-1/3+……1/n-1/(n+1)
=1-1/(n+1)
=n/(n+1)