Ta có:
$E=\dfrac{2019^{2019}+1}{2019^{2020}+1}$
$\to 2019E=\dfrac{2019^{2020}+2019}{2019^{2020}+1}$
$=\dfrac{2019^{2020}+1+2018}{2019^{2020}+1}$
$=1+\dfrac{2018}{2019^{2020}+1}$
Lại có:
$F=\dfrac{2019^{2020}+1}{2019^{2021}+1}$
$\to 2019F=\dfrac{2019^{2021}+2019}{2019^{2021}+1}$
$=\dfrac{2019^{2021}+1+2018}{2019^{2021}+1}$
$=1+\dfrac{2018}{2019^{2021}+1}$
Nhận thấy:
$\dfrac{2018}{2019^{2020}+1}>\dfrac{2018}{2019^{2021}+1}$
$\to 1+\dfrac{2018}{2019^{2020}+1}>1+\dfrac{2018}{2019^{2021}+1}$
$↔2019E>2019F$
$\to E>F$
