Đáp án:+Giải thích các bước giải:

 `A=1/1.2+1/3.4+1/5.6+...+1/101.102`

`A=1/1-1/2+1/3-1/4+1/5-1/6+...+1/101-1/102`

`A=(1+1/3+1/5+...+1/101)-(1/2+1/4+1/6+...+1/102)`

`A=(1+1/2+1/3+1/4+1/5+...+1/101+1/102) - 2(1/2+1/4+1/6+...+1/102)`

`A=(1+1/2+1/3+1/4+1/5+...+1/101+1/102)-(1 +1/2+1/3+1/4+...+1/51)`

`A=1/52+1/53+1/54+....+1/102`

`2A=(1/52+1/53+1/54+....+1/102) + (1/52+1/53+1/54+....+1/102)`

`2A=(1/52+1/102) + (1/53+1/101) + (1/54 +1/100) + ... + (1/102+1/52)`

`2A=154/52.102 +154/53.101 +154/54.100 + ... +154/102.52`

`2A=154 (1/52.102 +1/53.101 +1/54.100 + ... +1/102.52)`

`A=77*(1/52.102 +1/53.101 +1/54.100 + ... +1/102.52)`

`A=77*B`

`to A/B=77/1=77`

Vậy `A/B=77.`