Đáp án + giải thích bước giải :
`A = 1/2 (1 + 1/(1 . 3) ) (1 + 1/(2 . 4) ) (1 + 1/(3 . 5) ) ... (1 + 1/(2015 . 2017) )`
`⇔ A = 1/2 (1 + 1/3) (1 + 1/8) (1 + 1/15) ... (1 + 1/4064255)`
`⇔ A = 1/2 . 4/3 . 9/8 . 16/15 .... 4064256/4064255`
`⇔ A = 1/2 . (2 . 2)/3 . (3 . 3)/(2 . 4) . (4 . 4)/(3 . 5) ... (2016 . 2016)/(2015 . 2017)`
`⇔A = 1/2 . (2 . 3 . 4 .... 2016)/(1 . 2 . 3 .... 2015) . (2 . 3 . 4 .... 2016)/(3 . 4 . 5 .... 2017)`
`⇔ A = 1/2 . 2016 . 2/2017`
`⇔ A = 2016/2 . 2/2017`
`⇔ A = 2016/2017`
Vậy `A = 2016/2017`
