Thấy :
`1/2^2 <1 - 1/2`
`1/3^2 < 1/2 - 1/3`
`1/4^2 < 1/3 - 1/4 `
`1/5^2 < 1/4 - 1/5`
` ...`
`1/8^2 <1/7 - 1/8`
`→ 1/2^2 + 1/3^2 + 1/4^2 + ... + 1/8^2 < 1 - 1/2 + 1/2 - 1/3 + ... + 1/7 - 1/8`
`→ 1/2^2 + 1/3^2 + 1/4^2 + ... + 1/8^2 < 1 - 1/8 <1` `⇒ \text{đpcm}`