1/2X1/3+1/3X1/4+1/4X1/5+1/5X1/6+...............+1/99X1/100=? 求解题过程，谢谢！

1/2 X 1/3 + 1/3 X 1/4 + 1/4 X 1/5 + 1/5 X 1/6 +...............+ 1/99 X 1/100
= 1/(2 X 3) + 1/(3 X 4) + 1/(4 X 5) + ......+ 1/(99 X 100)
= (3 - 2)/(2 X 3) + (4 - 3)/(3 X 4) + (5 - 4