`55/56 + 71/72 + 89/90 + 109/110 + 131/132+ 155/156+181/182`

`= (1- 1/56) + (1- 1/72) + (1 - 1/90) + (1- 1/110) + (1 - 1/132) + (1 - 1/156) + (1 - 1/182)`

`= 1 - 1/56 + 1 - 1/72 + 1 - 1/90 + 1 - 1/110 + 1 - 1/132 + 1 - 1/156 + 1 - 1/182`

`= ( 1 + 1 + 1 + 1 + 1 + 1 + 1) - ( 1/56 + 1/72 + 1/90 + 1/110 + 1/132 + 1/156 + 1/182)`

`= 7 - ( 1/56 + 1/72 + 1/90 + 1/110 + 1/132 + 1/156 + 1/182) (1)`

Gọi `A =  1/56 + 1/72 + 1/90 + 1/110 + 1/132 + 1/156 + 1/182`

`⇒ A = 1/(7 xx 8) + 1/(9 xx 10) + 1/(10 xx 11) + 1/(11 xx 12) + 1/(12 xx 13) + 1/(13 xx 14)`

`A = 1/7 - 1/8 + 1/8 - 1/9 + 1/9 - 1/10 + 1/10 - 1/11 + 1/11 - 1/12 + 1/12 - 1/13 + 1/13 - 1/14`

`A = 1/7 - 1/14`

`A = 2/14 - 1/14`

`A = 1/14`

Thay `A` vào `(1), ta có:

`7 - 1/14 = 98/14 - 1/14 `

              `= 97/14`

$SoCutii$