A= `1/4` + `1/9` + `1/16` + `1/25` + `1/36` + `1/49` + `1/64` + `1/81`
A= `1/2^2` + `1/3^2` + `1/4^2` + `1/5^2` + `1.6^2` + `1/7^2` + `1/8^2` + `1/9^2`
Ta có (`1/2^2` + `1/3^2` + `1/4^2` + `1/5^2` + `1.6^2` + `1/7^2` + `1/8^2` + `1/9^2`) > `(1/2.3 + 1/3.4 + 1/4.5 + 1/5.6 + 1/6.7 + 1/7.8 + 1/8.9 + 1/9.10)`
⇒ `A` > `(1/2.3 + 1/3.4 + 1/4.5 + 1/5.6 + 1/6.7 + 1/7.8 + 1/8.9 + 1/9.10)`
Đặt biểu thức `(1/2.3 + 1/3.4 + 1/4.5 + 1/5.6 + 1/6.7 + 1/7.8 + 1/8.9 + 1/9.10)` = `B`
⇒ `B` = `1/2` - `1/3` + `1/3` - `1/4` + `1/4` - `1/5` + .... + `1/9` - `1/10`
⇒ `B` = `1/2` `-` `1/10`
⇒ `B` = `4/10` = `2/5`
Mà `A` > `B` (giả thiết đã cho trên)
⇒ `A` > `2/5` `(đpc/m)`