`A=4/{3xx6}+4/{6xx9}+...+4/{18xx21}`

`1/4A=1/{3xx6}+1/{6xx9}+...+1/{18xx21}`

`3/4A=3/{3xx6}+3/{6xx9}+...+3/{18xx21}`

`3/4A=1/3-1/6+1/6-1/9+...+1/18-1/21`

`3/4A=1/3-1/21`

`3/4A=2/7`

`A=2/7:3/4`

`A=8/21`

Vậy `A=8/21`

`B=1/2+1/6+1/12+1/20+1/30+1/42`

`B=1/{1xx2}+1/{2xx3}+1/{3xx4}+1/{4xx5}+1/{5xx6}+1/{6xx7}`

`B=1/1-1/2+1/2-1/3+1/3-1/4+...+1/6-1/7`

`B=1-1/7`

`B=6/7`

Vậy `B=6/7`

Công thức tổng quát: `k/{nxx(n+k)}=1/n-1/{n+k}` với `n,k` là số tự nhiên khác `0`

Ví dụ: `3/{3xx6}=3/{3xx(3+3)}=1/3-1/6`