(1+1/1×3)x (1+1/2×4)x(1+1/3×5)…(1+1/2014×2016) 27/09/2021 Bởi Brielle (1+1/1×3)x (1+1/2×4)x(1+1/3×5)…(1+1/2014×2016)
Đáp án + giải thích bước giải : `(1 + 1/(1 . 3) ) (1+1/(2 . 4) ) (1 + 1/(3 . 5) ) …. (1 + 1/(2014 . 2016) )` `= 4/3 . 9/8 . 16/15 ….. 4060225/4060224` `= (2 . 2)/(1 . 3) . (3 . 3)/(2 . 4) . (4 . 4)/(3 . 5) …. (2015 . 2015)/(2014 . 2016)` `= (2 . 2 . 3 . 3 . 4 . 4 … 2015 . 2015)/(1 . 3 . 2 . 4 . 3 . 5 … 2014 . 2016)` `= 2015/1008` Bình luận
`A= (1+1/(1 . 3)).(1+1/(2.4))(1+1/(3.5))……(1+1/(2011.2013)) ` $=\left(\frac{3}{3}+\frac{1}{3}\right)\left(\frac{8}{8}+\frac{1}{8}\right)….\left(\frac{4060224}{4060224} +\frac{1}{4060224}\right)$ $=\frac{4}{3}\cdot\frac{9}{8}\cdot…\cdot\frac{4060225}{4060224}$ $=\frac{4\cdot9\cdot….\cdot4060225}{3\cdot8\cdot….\cdot4060224}$ $=\frac{2\cdot2\cdot3\cdot3\cdot….\cdot2015\cdot2015}{1\cdot3\cdot2\cdot4\cdot….\cdot2014\cdot2016}$ $=\frac{2\cdot2015}{2016}=\frac{2015}{1008}$ Bình luận
Đáp án + giải thích bước giải :
`(1 + 1/(1 . 3) ) (1+1/(2 . 4) ) (1 + 1/(3 . 5) ) …. (1 + 1/(2014 . 2016) )`
`= 4/3 . 9/8 . 16/15 ….. 4060225/4060224`
`= (2 . 2)/(1 . 3) . (3 . 3)/(2 . 4) . (4 . 4)/(3 . 5) …. (2015 . 2015)/(2014 . 2016)`
`= (2 . 2 . 3 . 3 . 4 . 4 … 2015 . 2015)/(1 . 3 . 2 . 4 . 3 . 5 … 2014 . 2016)`
`= 2015/1008`
`A= (1+1/(1 . 3)).(1+1/(2.4))(1+1/(3.5))……(1+1/(2011.2013)) `
$=\left(\frac{3}{3}+\frac{1}{3}\right)\left(\frac{8}{8}+\frac{1}{8}\right)….\left(\frac{4060224}{4060224} +\frac{1}{4060224}\right)$
$=\frac{4}{3}\cdot\frac{9}{8}\cdot…\cdot\frac{4060225}{4060224}$
$=\frac{4\cdot9\cdot….\cdot4060225}{3\cdot8\cdot….\cdot4060224}$
$=\frac{2\cdot2\cdot3\cdot3\cdot….\cdot2015\cdot2015}{1\cdot3\cdot2\cdot4\cdot….\cdot2014\cdot2016}$
$=\frac{2\cdot2015}{2016}=\frac{2015}{1008}$