1/(a-1)+1/(a-1)(a-2)+1(a-2)(a-3).1/(a-99)(a-100)
=1/(a-1)+1/(a-1)-1/(a-2)+1/(a-2)-1/(a-3)+.+1/(a-99)-1/(a-100)
=2/(a-1)-1/(a-100)
=[2(a-100)-2]/(a-1)(a-100)
=(2a-202)/(a-1)(a-100)