Question

Tính A = 7 mũ 2024 - 7 mũ 2023 + 7 mũ 2022 - 7 mũ 2021 + ... + 7 mũ 2 - 7

Answer 1

\(A=7^{2024}-7^{2023}+7^{2022}-7^{2021}+...+7^2-7\)

=>\(7A=7^{2025}-7^{2024}+7^{2023}-7^{2022}+...+7^3-7^2\)

=>\(7A+A=7^{2025}-7^{2024}+7^{2023}-7^{2022}+...+7^3-7^2+7^{2024}-7^{2023}+...+7^2-7\)

=>\(8A=7^{2025}-7\)

=>\(A=\dfrac{7^{2025}-7}{8}\)