Đáp án + giải thích bước giải :
`1) 1/3 (x - 1) + 1/2 (x + 2) = 0,25`
`-> 1/3x - 1/3 + 1/2x + 1 = 0,25`
`-> (1/3x + 1/2x) + (-1/3 + 1) = 0,25`
`-> 5/6x + 2/3 = 0,25`
`-> 5/6x = (-5)/12`
`-> x = (-1)/2`
Vậy `x = (-1)/2`
`2) x - 1/4x = 60 - x + 1/4x`
`-> x - 1/4x - 60 + x - 1/4x = 0`
`-> x (1 - 1/4 + 1 - 1/4) - 60 = 0`
`-> x . 3/2 = 60`
`-> x = 60 : 3/2`
`-> x =40`
Vậy `x = 40`
`3) 1/3 + 1/6 + 1/10 + .... + 2/(x (x + 1) ) = 2016/2017`
`-> 2/6 + 2/12 + 2/20 + ... + 2/(x (x + 1) ) = 2016/2017`
`-> 2 [1/6 + 1/12 + 1/20 +...+ 1/(x (x + 1) )] = 2016/2017`
`-> 2 [1/(2 . 3) + 1/(3 . 4) + 1/(4 . 5) + ... + 1/(x (x + 1) ) ] = 2016/2017`
`-> 2 [1/2 - 1/3 + 1/3 - 1/4 + 1/4 - 1/5 + ... + 1/x - 1/(x + 1) ] = 2016/2017`
`-> 2 [1/2 + (- 1/3 + 1/3 - 1/4 + 1/4 - 1/5 + ... + 1/x) - 1/(x + 1)] = 2016/2017`
`-> 2 [1/2 - 1/(x + 1)] = 2016/2017`
`-> 1/2 - 1/(x + 1) = 1008/2017`
`-> 1/(x + 1) = 1/4034`
`-> x + 1 = 4034`
`-> x = 4033`
Vậy `x = 4033`
