Ta có :
`1/2^2 < 1/{1 . 2}`
`1/3^2 < 1/{2 . 3}`
`....`
`1/50^2 < 1/{49 . 50}`
`-> 1/2^2 +1/3^2 +1/4^2 + ... +1/50^2 < 1/{1.2} + 1/{2.3} +1/{3.4} + .... + 1/{49.50}`
`-> 1/2^2 +1/3^2 +1/4^2 + ... +1/50^2 < 1 - 1/2 +1/2 - 1/3 +1/3 -1/4 + ... +1/49 -1/50`
`-> 1/2^2 +1/3^2 +1/4^2 + ... +1/50^2 < 1 - 1/50`
`-> 1/1^2 + 1/2^2 +1/3^2 +1/4^2 + ... +1/50^2 < 1 +1 - 1/50 = 2 - 1/50`
Mà `2 -1/50 < 2`
`-> A = 1/1^2 + 1/2^2 +1/3^2 +1/4^2 + ... +1/50^2 < 2`
Vậy `A <2`
