1／n(n+1) = 1/n - 1/(n + 1)
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)