Ta có :
`A = 1/2020( 1 + 1/2 + 1/3 + .... + 1/2020)`
`Đặt 1 + 1/2 + 1/3 + .... + 1/2020 = t`
`⇒ A = 1/2020 . t = t/2020`
Lại có :
`B = 1/2021( 1 + 1/2 + 1/3 + ... + 1/2021)`
`= 1/2021(1 + 1/2 + 1/3 + .... + 1/2020 + 1/2021)`
`= 1/2021( t + 1/2021)`
`= 1/2021 . t + 1/(2021^2)= t/2021 + 1/(2021^2)`
Ta lấy A - B
`= t/2020 - t/2021 - 1/(2021^2)`
`= t/(2020 . 2021) - 1/(2021^2)`
`=2021t/(2020.2021^2) - 2020/(2020.2021^2)`
`=(2021t - 2020)/(2020.2021^2) > 0`
`⇒ A > B`