Question

CMR:   A=3 + 3^2 + 3^3 + .... + 3^2012 + 3^2013 CHIA HẾT CHO 13

Answer 1

\(A=3+3^2+3^3+...+3^{2012}+3^{2013}\)

\(=\left(3+3^2+3^3\right)+...+\left(3^{2011}+3^{2012}+3^{2013}\right)\)

\(=3\left(1+3+3^2\right)+...+3^{2011}\left(1+3+3^2\right)\)

\(=\left(1+3+3^2\right)\left(3+...+3^{2011}\right)\)

\(=13\left(3+...+3^{2011}\right)\)

Vì  13 chia hết cho 13 nên   \(13\left(3+...+3^{2011}\right)\) chia hết cho 13

Vậy A chia hết cho 13

Answer 2

A=(3+3²+3³)+(3⁴+3⁵+3⁶)+...+(3²⁰¹¹+3²⁰¹²+3²⁰¹³)

A=3(1+3+3²)+3⁴(1+3+3²)+...+3²⁰¹¹(1+3+3²)

A=3.13+3^4.13+...+3^2011.13

A=13(3+3^4+...+3^2011)chia hết cho 13

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