解：1/1X2+1/2X3+1/3X4+...+1/99X100 =（1-1/2）+(1/2-1/3)+(1/3-1/4)+...+(1/99-1/100) =1-1/2+1/2-1/3+1/3-1/4+...+1/99-1/100 （中间两项两项正负抵消）=1-1/100 =99/100
