Bài `1:`
`3/(5 . 8) + 11/(8 . 19) + 12/(19 . 31) + 70/(31 . 101) + 11/(101 . 200)`
`= 1/5 - 1/8 + 1/8 - 1/19 + 1/19 - 1/31 + 1/31 - 1/101 + 1/101 - 1/200`
`= 1/5 - (1/8 - 1/8) - (1/19 - 1/19) - (1/31 - 1/31) - (1/101 - 1/101) - 1/200`
`= 1/5 - 0 - 0 - 0 - 0 - 1/200`
`= 1/5 - 1/200`
`= 39/200`
Bài `2:`
`@ 1/1^2 < 1/(1 . 2)`
`@ 1/2^2 < 1/(2 . 3)`
`@ 1/4^2 < 1/(3 . 4)`
`@ ...`
`@ 1/n^2 < 1/((n - 1) . n)`
`=> 1/1^2 + 1/2^2 + 1/3^4 + ... + 1/n^2 < 1/(1 . 2) + 1/(2 . 3) + 1/(3 . 4) + ... + 1/((n - 1) . n)`
`=> 1/1^2 + 1/2^2 + 1/3^4 + ... + 1/n^2 < 1 - 1/n`
`Mà: 1/1^2 + 1/2^2 + 1/3^4 + ... + 1/n^2 < 1 - 1/n < 2`
`=> 1/1^2 + 1/2^2 + 1/3^4 + ... + 1/n^2 < 2` `(đpcm)`
