`A= 1/2^2 + 1/4^2 + 1/6^2 +...+1/100^2`
`A= 1/2^2 ( 1+ 1/2^2 1/3^2 +...+1/50^2)`
Đặt `B = 1 +1/2^2 + 1/3^2 + ....+1/50^2`
`B = 1 + 1/2.2 + 1/3.3 +...+1/50.50`
`B< 1+ 1/1.2 + 1/2.3 +...+1/49.50`
`B < 1+ 1/1 - 1/2 + 1/2 -1/3+...+1/49 - 1/50`
`B< 1+ 1/1 - 1/50`
`=> A < 1/2^2 ( 1 + 1 -1/50) < 1/2`
Vậy `A <1/2`