Question

Chứng minh rằng:A=2 + 2^2 + 2^3 +..............+ 2^2022 chia hết cho 42

giúp e vs bài hồi sáng hôm nay e thi mà ko bt lm

Answer 1

\(A=\left(2+2^2+2^3+2^4+2^5+2^6\right)+...+\left(2^{2017}+2^{2018}+2^{2019}+2^{2020}+2^{2021}+2^{2022}\right)\\ A=\left(2+2^2+2^3+2^4+2^5+2^6\right)\left(1+...+2^{2017}\right)\\ A=126\left(1+...+2^{2017}\right)⋮42\left(126⋮42\right)\)