1/1x2x3+1/2x3x4+....+1/98x99x100 =1/2 × [(1/1x2 - 1/2x3)+(1/2x3 - 1/3x4)+(1/3x4 - 1/4x5)+......+(1/98x99 - 1/99x100)]=1/2 × [1/1x2 - 1/99x100]=1/2 × 4994/9900=2497/9900
