Đặt `A = 1/2^2 + 1/3^2 +....+1/2019^2`
Ta có: `1/2^2 = 1/2.2 < 1/1.2`
`1/3^2 = 1/3.3 < 1/2.3`
............................................
`1/2019^2 = 1/2019.2019 < 1/2018.2019`
=> `1/2^2 + 1/3^2 +...+ 1/2019^2 < 1/1.2 +1/2.3 + 1/3.4+...+1/2018.2019`
=> `A < 1 - 1/2+1/2 -1/3+1/3-1/4+...+1/2018 - 1/2019`
=> `A < 1-1/2019`
Nhận thấy `1-1/2019 < 1/2019` mà `A < 1-1/2019`
=> `A < 1/2019`
Vậy `A < 1/2019`
