100*101/1+101*102/1+…+n(n+1)/1

100*101/1+101*102/1+…+n(n+1)/1
=(1/100-1/101)+(1/101-1/102)+...+[1/n-1/(n+1)]
=1/100-1/(n+1)
=(n-99)/[100(n+1)]