Đáp án:

Giải thích các bước giải:

 Đây nha 

Ta có :

`Q = 1/5 - 2/5^2 + 3/5^3 - ... + 2021/5^2021 - 2022/5^2022`

`⇒ 5Q = 1 - 2/5  +3/5^2 - ... + 2021/5^2020 - 2022/5^2021`

`⇒ 5Q  +Q = (1 - 2/5  +3/5^2 - ... + 2021/5^2020 - 2022/5^2021) + (1/5 - 2/5^2 + 3/5^3 - ... + 2021/5^2021 - 2022/5^2022)`

`⇒ 6Q = 1 - 1/5 + 1/5^2 - ... + 1/5^2020 - 1/5^2021 - 2022/5^2022`

`⇒ -6/5Q = -1/5 + 1/5^2 - 1/5^3 + ... - 1/5^2021 - 1/5^2022 - 2022/5^2023`

`⇒ 6Q - (-6/5Q) = (1 - 1/5 + 1/5^2 - ... + 1/5^2020 - 1/5^2021 - 2022/5^2022) - (-1/5 + 1/5^2 - 1/5^3 + ... - 1/5^2021 - 1/5^2022 - 2022/5^2023)`

`⇒ 36/5Q = 1- 2021/5^2022 + 2022/5^2023 = 1 - 1/5^2022(2021 - 2022/5) < 1`

`⇒ Q < 5/35 (đpcm)`