\(1+3+3^2+3^3+...+3^{2023}\)
\(=\left(1+3\right)+\left(3^2+3^3\right)+...+\left(3^{2022}+3^{2023}\right)\)
\(=4+3^2\cdot\left(1+3\right)+...+3^{2022}\cdot\left(1+3\right)\)
\(=4+4\cdot3^2+4\cdot3^4+....+4\cdot3^{2022}\)
\(=4\cdot\left(1+3^2+3^4+...+3^{2022}\right)\)
Mà: \(4\cdot\left(1+3^2+3^4+...+3^{2022}\right)\) ⋮ 4
\(\Rightarrow1+3+3^2+3^3+....+3^{2023}\) ⋮ 4
Đặt \(A=1+3+3^2+...+3^{2023}\)
\(A=4+3^2\left(1+3\right)+...+3^{2022}\left(1+3^{2021}\right)\)
\(=4\left(1+3^2+...+3^{2022}\right)⋮4\)
\(\Rightarrow A⋮4\left(đpcm\right)\)
1+3+3^2+...........+3^2023
=(1+3)+(3^2+3^3)+.........+(3^2022+3^2023)
=4+3^2(1+3)+.......+3^2022(1+3)
=4(3^2+3^4+......+3^2022)chia hết cho 4
=>1+3+3^2+......................................................................+3^2023 chia hết cho 4
unicorn in taming 50/50