tính 2/4.7+2/7.10+2/10.13+...+2/73.76

Answer

Đặt: `2/{4 . 7} + 2/{7 . 10} + 2/{10 . 13} + ... + 2/{73 . 76} = A`

`A = 2/{4 . 7} + 2/{7 . 10} + 2/{10 . 13} + ... + 2/{73 . 76}`

`A = 3/3 . (2/{4 . 7} + 2/{7 . 10} + 2/{10 . 13} + ... + 2/{73 . 76})`

`A = 2/3 . (3/{4 . 7} + 3/{7 . 10} + 3/{10 . 13} + ... + 3/{73 . 76})`

`A = 2/3 . (1/4 - 1/7 + 1/7 - 1/10 + 1/10 - 1/13 + ... + 1/73 - 1/76)`

`A = 2/3 . (1/4 - 1/7 + 1/7 - 1/10 + 1/10 - 1/13 + ... + 1/73 - 1/76)`

`A = 2/3 . (1/4 - 1/76)`

`A = 2/3 . 9/38`

`A = 3/19`

Vậy `A = 3/19`