`A = 3/4^2 + 3/5^2 + 3/6^2 + ... + 3/2020^2`
`A = 3/4^2 + 3/5^2 + 3/6^2 + ... + 3/2020^2 < 3/3.4 + 3/4.5 + 3/5.6 + ... + 3/2019.2020`
`A = 3/4^2 + 3/5^2 + 3/6^2 + ... + 3/2020^2 < 3(1/3.4 + 1/4.5 + 1/5.6 + ... + 1/2019.2020)`
`A = 3/4^2 + 3/5^2 + 3/6^2 + ... + 3/2020^2 < 3(1/3 - 1/4 + 1/4 - 1/5 + 1/5 - 1/6 + ... + 1/2019 - 1/2020)`
`A = 3/4^2 + 3/5^2 + 3/6^2 + ... + 3/2020^2 < 3(1/3 - 1/2020)`
`A = 3/4^2 + 3/5^2 + 3/6^2 + ... + 3/2020^2 < 3(1 - 2020 - 3 . 1)/6060`
`A = 3/4^2 + 3/5^2 + 3/6^2 + ... + 3/2020^2 < 3 . 2017/6060`
`A = 3/4^2 + 3/5^2 + 3/6^2 + ... + 3/2020^2 < 2017/6060`
Vì `2017/6060 notin ZZ`
Mà `A < 2017/6060`
`=> A notin ZZ`
Vậy `, A` không phải là số nguyên `.`