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