`A=1/1.2 + 1/2.3 + ... + 1/9.10`
`=1-1/2+1/2-1/3+...+1/9-1/10`
`=(1+1/3+1/5+1/7+1/9)-(1/2+1/4+1/6+1/10)`
`(1+1/2+1/4+1/5+1/6+1/7+1/8+1/9+1/10)-2.(1/2+1/4+1/6+1/8+1/10)`
`=(1+1/2+1/1/4+1/5+1/6+1/7+1/8+1/9+1/10)-(1+1/2+1/3+1/4+1/5`
`=1/6+1/7+1/8 + 1/9 +1/10` (1)
`B=1/6.10 + 1/7.9 + 1/8.8 + 1/9.7 + 1/10.6`
`=>16B=16.(1/6.10 + 1/7.9 + 1/8.8 + 1/9.7 + 1/10.6)`
`=16/6.10 + 16/7.9 + 16/8.8 + 16/9.7 + 16/10.6`
`=1/6+1/7 + 1/7+1/9 + 1/8+1/8 + 1/9+1/7 +1/10+1/6`
`=2(1/6+1/7+1/8 + 1/9 +1/10)`
` <=> 8B=1/6+1/7+1/8 + 1/9 +1/10 ` (2)
Từ `(1)` và `(2):`
`A=8B=1/6+1/7+1/8 + 1/9 +1/10`
` <=> A/B=8 `