tínhnhanh A= 1/7+1/8+1/9+1/10+1/11+1/12+1/14+1/15+1/18+1/22+1/24+1/28+1/33

Ta thấy:

`1/7 + 1/14 + 1/28 = (4+2+1)/28 = 1/4`

`1/8 + 1/12 + 1/24 = (3+2+1)/24 = 1/4`

`1/11 + 1/22 + 1/33 = (6+3+2)/66 = 1/6`

`1/9 + 1/18 = (2+1)/18 = 1/6`

Mà `1/4 + 1/4 = 1/2` và `1/6 + 1/6 = 1/3`

Nên:

`1/10 + 1/13 + 1/15 + 1/2 + 1/3 `

`=1/10 + 1/13 + 1/15 + 5/10 + 5/15 `

`=6/10 + 6/15 + 1/13 `

`=3/5 + 2/5 + 1/13`

`=1+ 1/13 `

`=14/13`