$\frac{x+19}{2019}$ $\frac{x+18}{2018}$ $\frac{x+17}{2017}$ +…..+ $\frac{x+1}{2001}$ =19

Đáp án + Giải thích các bước giải:

`(x+19)/2019 + (x+18)/2018 + (x+17)/2017 + … + (x+1)/2001 = 19`

`to (x+19)/2019 + (x+18)/2018 + (x+17)/2017 + … + (x+1)/2001 – 19 = 0`

`to ( (x+19)/2019 – 1 ) + ( (x+18)/2018 – 1 ) + ( (x+17)/2017 – 1 ) + … + ( (x+1)/2001 – 1 ) = 0 `

`to (x+19-2019)/2019 + (x+18-2018)/2018 + (x+17-2017)/2017 + … + (x+1-2001)/2001 = 0`

`to (x-2000)/2019 + (x-2000)/2018 + (x-2000)/2017 + … + (x-2000)/2001 = 0`

`to (x-2000) . (1/2019+1/2018+1/2017+…+1/2001)=0`

Mà `1/2019+1/2018+1/2017+…+1/2001 ne 0`

`to x-2000=0`

`to x=2000`

Vậy `x=2000`