`\color{#1c1c1c}{ccI}^(\color{#363636}{t}^(\color{#4f4f4f}{s}^(\color{#696969}{m}^(\color{#828282}{e}^(\color{#9c9c9c}{ccF}^(\color{#b5b5b5}{r}^(\color{#cfcfcf}{e}^\color{#eee9e9}{d})))))))`

`A = 1/5 - 2/5^2 + 3/5^3 - 4/5^4 + ... - 2022/5^2022`

`5A = 1 - 2/5 + 3/5^2 - 4/5^3 + ... - 2022/5^2021`

`5A + A = (1 - 2/5 + 3/5^2 - 4/5^3 + ... - 2022/5^2021) + (1/5 - 2/5^2 + 3/5^3 - 4/5^4 + ... - 2022/5^2022)`

`6A = 1 - 1/5 + 1/5^2 - 1/5^3 + 1/5^4 - ... - 1/5^2021 - 2022/5^2022`

`30A = 5 - 1 + 1/5 - 1/5^2 + 1/5^3 - ... - 1/5^2020 - 2022/5^2021`

`30A + 6A = (5 - 1 + 1/5 - 1/5^2 + 1/5^3 - ... - 1/5^2020 - 2022/5^2021) + (1 - 1/5 + 1/5^2 - 1/5^3 + 1/5^4 - ... - 1/5^2021 - 2022/5^2022)`

`36A = 5 - 2023/5^2021 - 2022/5^2022`

`A = 5/36 - 2023/(5^2021 . 36) - 337/(5^2022 . 6)`

     Mà `5/36 - 2023/(5^2021 . 36) - 337/(5^2022 . 6) < 5/36`

     `=> A < 5/36`