Đáp án: `4028/2015`
Giải thích các bước giải:
Ta có:
`(1+1/(1.3)) (1+1/(2.4)) (1+1/(3.5)) (1+1/(4.6)) ... (1+1/(2013.2015))`
`= 4/(1.3) . 9/(2.4) . 16/(3.5) . 25/(4.6) ... 4056196/(2013.2015)`
`= (2^2)/(1.3) . (3^2)/(2.4) . (4^2)/(3.5). (5^2)/(4.6) ..... (2014^2)/(2013.2015)`
`= (2².3².4².5².....2014²)/(1.3.2.4.3.5.4.6.....2013.2015)`
`= ((2.3.4.5....2014)(2.3.4.5...2014))/((2.3.4...2013)(3.4.5.6....2015))`
`= (2014.2)/2015 = 4028/2015`
