2 mũ 2023 - 2 mũ 2022 - 2 mũ 2021-...- 2 mũ 1 - 1

Đáp án: ${2^{2023}} - {2^{2022}} - {2^{2021}} - ... - {2^1} - 1 = 1$

Giải thích các bước giải:

$\begin{array}{l}
A = {2^{2023}} - {2^{2022}} - {2^{2021}} - ... - {2^1} - 1\\
 = {2^{2023}} - \left( {{2^{2022}} + {2^{2021}} + ... + {2^1} + 1} \right)\\
 = {2^{2023}} - B\\
Dat:B = {2^{2022}} + {2^{2021}} + ... + {2^1} + 1\\
 \Leftrightarrow 2.B = {2^{2023}} + {2^{2022}} + ... + {2^2} + 2\\
 \Leftrightarrow 2B - B\\
 = {2^{2023}} + {2^{2022}} + ... + {2^2} + 2\\
 - \left( {{2^{2022}} + {2^{2021}} + ... + {2^1} + 1} \right)\\
 \Leftrightarrow B = {2^{2023}} + {2^{2022}} + ... + {2^2} + 2\\
 - {2^{2022}} - {2^{2021}} - ... - {2^1} - 1\\
 \Leftrightarrow B = {2^{2023}} - 1\\
 \Leftrightarrow A = {2^{2023}} - B\\
 = {2^{2023}} - \left( {{2^{2023}} - 1} \right)\\
 = {2^{2023}} - {2^{2023}} + 1\\
 = 1\\
Vậy\,{2^{2023}} - {2^{2022}} - {2^{2021}} - ... - {2^1} - 1 = 1
\end{array}$