Question

so sánh A=1/2²+1/3²+1/4²+...+1/2023² với 1

Answer 1

`A= 1/(2^2) + 1/(3^2) + 1/(4^2) + ... + 1/(2023^2)`

Biết: `1/(2^2) < 1/(1 . 2)`

`1/(3^2) < 1/(2 . 3)`

`1/(4^2) < 1/(3 . 4)`

`...`

`1/(2023^2) < 1/(2022 . 2023)`

Suy ra: `A < 1/(1 . 2) + 1/(2 . 3) + 1/(3 . 4) + ... + 1/(2022 + 2023)`

`= 1 - 1/2 + 1/2 - ... - 1/2022 + 1/2022 - 1/2023`

`= 1 - 1/2023`

`= 2022/2023 < 2023/2023 = 1`

Do đó: `A < 1`