1/1*2+1/2*3+1/3*4+……+1/99*100
=(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
=1-1/100
=99/100
因为,1/2-1/3=3/6-2/6=1/6=1/2*3,所以1/2*3=1/2-1/3；
1/3-1/4=4/12-3/12=1/12=1/3*4,所以1/3*4=1/3-1/4；
以此类推.我要算式+得数你要的算式+得数就是=(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=1-1/100=99/100可以了吗？望采纳！