A= 2018+2017/2+2016/3+....+1/2018 --------------------------------------------------- 1/2+1/3+1/4+....+1/2019

Đáp án:

 

Giải thích các bước giải:

`A = (2018 + 2017/2 + 2016/3 + ... + 1/2018)/(1/2 + 1/3 + 1/4 + ... + 1/2019)`

Ta có `:`

`(2018 + 1) + (2017/2 + 1) + (2016/3 + 1) + ... + (1/2018 + 1)- 2018` (vì có `2018` số hạng)

`= 2019 + (2017/2 + 2/2) + (2016/3 + 3/3) + ... + (1/2018 + 2018/2018) - 2018`

`= (2019 - 2018) + 2019/2 + 2019/3 + .... + 2019/2018`

`= 1 + 2019/2 + 2019/3 + .... + 2019/2018`

`= 2019/2 + 2019/3 + .... + 2019/2018 + 2019/2019`

`= (1/2 + 1/3 + ... + 1/2018 + 1/2019) xx 2019`

Thay `2018 + 2017/2 + 2016/3 + ... + 1/2008` thành `(1/2 + 1/3 + ... + 1/2018 + 1/2019)` `,` ta có `:`

`A = ((1/2 + 1/3 + ... + 1/2018 + 1/2019) xx 2019)/(1/2+ 1/3 + ... + 1/2018 + 1/2019)`

`A = (1 xx 2019)/1`

`A = 2019`

Vậy `A = 2019`