Đáp án:
Giải thích các bước giải:
$A=\dfrac{10^{2020}+1}{10^{2019}+1}$
$ $
$⇒\dfrac{A}{10}=\dfrac{10^{2020}+1}{10^{2020}+10}=\dfrac{10^{2020}+10-9}{10^{2020}+10}=1-\dfrac{9}{10^{2020}+10}$
$ $
$B=\dfrac{10^{2021}+1}{10^{2020}+1}$
$ $
$⇒\dfrac{B}{10}=\dfrac{10^{2021}+1}{10^{2021}+10}=\dfrac{10^{2021}+10-9}{10^{2021}+10}=1-\dfrac{9}{10^{2021}+10}$
$ $
Mà $\dfrac{9}{10^{2020}+10}>\dfrac{9}{10^{2021}+10}$
$ $
$⇒1-\dfrac{9}{10^{2020}+10}<1-\dfrac{9}{10^{2021}+10}$
$ $
$⇒\dfrac{A}{10}<\dfrac{B}{10}$
$ $
$⇒A<B$