Ta có: `1/3^2 < 1/2.3`
`1/4^2 < 1/3.4`
`1/5^2 < 1/4.5`
`...............`
`1/2020^2 < 1/2019.2020`
`=> 1/3^2 + 1/4^2 + 1/5^2 +...+ 1/2020^2 < 1/2.3 + 1/3.4 + 1/4.5+...+1/2019.2020`
`=> A< 1/2 - 1/3 + 1/3 -1/4+...+1/2019 - 1/2020`
`=> A< 1/2 - 1/2020 < 1/2`
Vậy `A< 1/2`