Question

Cho \(A=2+2^{2}+2^{3}+2^{4}+...+2^{2019}+2^{2020}.\)Chứng tỏ rằng \(A⋮3\).
Mình đang cần gấp,mai mình phải nộp!

Answer 1

A=\(\left(2+2^2\right)+\left(2^3+2^4\right)+...+\left(2^{2019}+2^{2020}\right)\\ 2^2\left(1+2\right)+2^3\left(1+2\right)+...+2^{2019}\left(1+2\right)\\ 3\left(2^2+2^3+...+2^{2019}\right)\)

=> A \(⋮\) 3