Question

Cho A = 3+3³+3⁵+ ... + 3¹⁹⁹¹. Chứng minh A ⋮ 13. 

Answer 1

Tham khảo

https://hoc24.vn/cau-hoi/c-3-33-35-31991-chia-het-cho-13-va-41.2492703297984

Answer 2

\(A=\left(3+3^2+3^3\right)+\left(3^4+3^5+3^6\right)+...+\left(3^{1989}+3^{1990}+3^{1991}\right)\\ A=3\left(1+3+3^2\right)+3^4\left(1+3+3^2\right)+...+3^{1989}\left(1+3+3^2\right)\\ A=\left(1+3+3^2\right)\left(3+3^4+...+3^{1989}\right)\\ A=13\left(3+3^4+...+3^{1989}\right)⋮13\)

Answer 3

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