Đáp án:
\[A = 2025\]
Giải thích các bước giải:
Ta có:
\(\begin{array}{l}
n = {2^{2019}} - {2^{2018}} - {2^{2017}} - {2^{2016}} - .... - 2 - 1\\
m = {2^{2018}} + {2^{2017}} + {2^{2016}} + .... + 2 + 1\\
\Leftrightarrow 2m = {2^{2019}} + {2^{2018}} + {2^{2017}} + .... + {2^2} + 2\\
\Rightarrow 2m - m = \left( {{2^{2019}} + {2^{2018}} + {2^{2017}} + .... + {2^2} + 2} \right) - \left( {{2^{2018}} + {2^{2017}} + {2^{2016}} + .... + 2 + 1} \right)\\
\Leftrightarrow m = {2^{2019}} - 1\\
\Rightarrow n = {2^{2019}} - m = {2^{2019}} - \left( {{2^{2019}} - 1} \right) = 1\\
A = {3^n} + {2^n} + {2020^n} = 3 + 2 + 2020 = 2025
\end{array}\)
