Giải thích các bước giải:
Ta có:
\(\begin{array}{l}
A = 1 + {2^1} + {2^2} + {2^3} + .... + {2^{2020}}\\
\Rightarrow 2A = 2.\left( {1 + {2^1} + {2^2} + {2^3} + .... + {2^{2020}}} \right)\\
\Leftrightarrow 2A = 2 + {2^2} + {2^3} + {2^4} + .... + {2^{2021}}\\
\Rightarrow 2A - A = \left( {2 + {2^2} + {2^3} + {2^4} + .... + {2^{2021}}} \right) - \left( {1 + {2^1} + {2^2} + {2^3} + .... + {2^{2020}}} \right)\\
\Leftrightarrow A = {2^{2021}} - 1\\
B = {2^{2020}} - \left( {1 + {2^1} + {2^2} + {2^3} + .... + {2^{2020}}} \right)\\
\Leftrightarrow B = {2^{2020}} - A\\
\Leftrightarrow B = {2^{2020}} - \left( {{2^{2021}} - 1} \right)\\
\Leftrightarrow B = {2^{2020}} + 1 - {2^{2021}}
\end{array}\)
