Đáp án:
$\begin{array}{l}
A = {2019^{2020}} - {2019^{2019}} + {2019^{2018}} - ...\\
+ {2019^2} - 2019\\
\Rightarrow 2019.A = {2019^{2021}} - {2019^{2020}} + {2019^{2019}} - ...\\
+ {2019^3} - {2019^2}\\
\Rightarrow A + 2019A = {2019^{2021}} - 2019\\
\Rightarrow 2020.A = {2019^{2021}} - 2019\\
\Rightarrow A = \dfrac{{{{2019}^{2021}} - 2019}}{{2020}}
\end{array}$