Question

一乘二分之一加二乘三分之一加.............加一百九十九乘二百分之一，怎么计算啊，那位大侠帮帮我啊？

Answer 1

1/(1*2)+1/(2*3)+1/(3*4)+1/(4*5)-~~~~~~~~~1/(199*200)
=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5~~~~~~~~+1/199-1/200
=1-1/200
=199/200

Answer 2

1/n(n+1)=1/n-1/(n+1)
因此
一乘二分之一加二乘三分之一加.............加一百九十九乘二百分之一
=1-1/2+1/2-1/3+1/3-1/4+……+1/199-1/200
=1-1/200
=199/200