Ta có :
`T= 2/2 + 3/(2^2) + .... +2021/(2^2020)`
`2T = 4/2 + 3/2 + .......+ 2021/(2^2019)`
`⇒ T=2+ 1/2 + 1/(2^2) +....+ 1/(2^2018)`
Đặt `1/2 + 1/(2^2) +....+ 1/(2^2018) = A`
`2A = 1/1+ 1/2 + 1/(2^2) +....+ 1/(2^2017)`
`⇒ A = 1/1 - 1/2^2018`
`⇒ T = 2 + 1/1 - 1/(2^2018)`
`⇒ T - 3= -1/(2^2018) < 0` ( đpcm )