Question

[Trần Trung Huy]

A= 2^3+2^4+2^5+2^6+2^7+2^8+...+2^2021 tìm số dư chia hết cho 3

Answer 1

[Đoàn Đức Hà]

\(A=2^3+2^4+2^5+...+2^{2021}\)

\(=2^3+\left(2^4+2^5\right)+\left(2^6+2^7\right)+...+\left(2^{2020}+2^{2021}\right)\)

\(=2^3+2^4\left(1+2\right)+2^6\left(1+2\right)+...+2^{2020}\left(1+2\right)\)

\(=2^3+3\left(2^4+2^6+...+2^{2020}\right)\equiv2^3\left(mod3\right)\equiv2\left(mod3\right)\).