Ta có: `1/2^2 < 1/1.2`
`1/3^2 < 1/2.3`
`1/4^2 < 1/3.4`
...
`1/100^2 < 1/99.100`
`=> 1/2^2 + 1/3^2 + 1/4^2 + ... + 1/100^2 < 1/1.2 + 1/2.3 + 1/3.4 + ... + 1/99.100`
`=> 1/2^2 + 1/3^2 + 1/4^2 + ... + 1/100^2 < 1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + ... + 1/99 - 1/100`
`=> 1/2^2 + 1/3^3 + 1/4^2 + ... + 1/100^2 < 1 - 1/100 < 1`
`=> 1/2^2 + 1/3^2 + 1/4^2 + ... + 1/100^2 < 1` (đpcm)`
HỌC TỐT!
