Question

Cho A=1+2+2^2+2^3+...+2^2023 Hãy chứng tỏ A chia hết cho 3

Answer 1

\(A=\left(1+2\right)+2^2\left(1+2\right)+...+2^{2022}\left(1+2\right)\)

\(=3\left(1+2^2+...+2^{2022}\right)⋮3\)

Answer 2

A=(1+2)+(2^2+2^3)+...+(2^2022+2^2023)

A=3+2^2.(1+2) +...+2^2022.(1+2)

A=3+2^2.3+...+2^2022.3

A=(1+2^2+...+2^2022)⋮3

=>A⋮3