CMR: 1/2²+1/3²+1/4²+...+1/2018²

Đáp án+Giải thích các bước giải:

Ta có :

`1/2^2 < 1/{1.2}`

`1/3^2 < 1/{2.3}`

`1/4^2 < 1/{3.4}`

...

`1/2018^2 < 1/{2017 . 2018}`

`⇒` `1/2^2 + 1/3^2 + 1/4^2 + ... + 1/2018^2 < 1/{1.2} + 1/{2.3} + 1/{3.4} + ... + 1/{2017 . 2018}`

`⇒` `1/2^2 + 1/3^2 + 1/4^2 + ... + 1/2018^2 < 1/1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + ... + 1/2017 - 1/2018`

`⇒` `1/2^2 + 1/3^2 + 1/4^2 + ... + 1/2018^2 < 1 - 1/2018`

`⇒` `1/2^2 + 1/3^2 + 1/4^2 + ... + 1/2018^2 < 2017/2018`

Mà `2017/2018 < 1`

`⇒` `1/2^2 + 1/3^2 + 1/4^2 + ... + 1/2018^2 < 1` `(đpcm)`