Đặt `A =2/{2 . 3} + 2/{ 3 . 4} + 2/{4 . 5} + ... + 2/{49 . 50}`
`-> A = 2(1/{2 . 3} + 1/{ 3 . 4} + 1/{4 . 5} + ... + 1/{49 . 50})`
`-> A =2( 1/2 -1/3 +1/3 -1/4 +1/4 -1/5 + ... + 1/49 -1/50 )`
`-> A = 2(1/2 -1/50)`
`-> A = 1 - 2/50 = 48/50 = 24/25`
Vậy `2/{2 . 3} + 2/{ 3 . 4} + 2/{4 . 5} + ... + 2/{49 . 50} = 24/25`