1/2x1/3+1/3x1/4+1/4x1/5+1/5x1/6+.....1/99x1/100=(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+(1/5-1/6)+......+(1/99-1/100)=1/2-1/100=50/100-1/100=49/100谢谢,请采纳