Question

A = 3 + 3² + 3³ + 3⁴ + ... + 3²⁹ + 3³⁰.Chứng tỏ A chia hết cho 13

Answer 1

 

=> A = 3(1 + 3 + 3²) + 3⁴(1 + 3 + 3²) + ..... + 3²⁸(1 + 3 + 3²)

=> A = 3.13 + 3⁴.13 + ..... + 3²⁸.13

=> A = 13( 3 + 3⁴ + ..... + 3²⁸) chia hết cho 13

 

Answer 2

Ta có : A = 3 + 3² + 3³ + ..... + 3²⁹ + 3³⁰

=> A = (3 + 3² + 3³) + (3⁴ + 3⁵ + 3⁶) + ...... + (3²⁸ + 3²⁹ + 3³⁰)

=> A = 3(1 + 3 + 3²) + 3⁴(1 + 3 + 3²) + ..... + 3²⁸(1 + 3 + 3²)

=> A = 3.13 + 3⁴.13 + ..... + 3²⁸.13

=> A = 13( 3 + 3⁴ + ..... + 3²⁸) chia hết cho 13

Answer 3

\(A=3+3^2+3^3+3^4+...+3^{29}+3^{30}\)

\(A=\left(3+3^2+3^3\right)+\left(3^4+3^5+3^6\right)+...+\left(3^{28}+3^{29}+3^{30}\right)\)

\(A=3\times\left(1+3+3^2\right)+3^4\times\left(1+3+3^2\right)+...+3^{28}\left(1+3+3^2\right)\)

\(A=\left(1+3+3^2\right)\times\left(3+3^4+...+3^{28}\right)\)

\(A=13\times\left(3+3^4...+3^{28}\right)\)

Có : \(13\times\left(3+3^4+...+3^{28}\right)⋮13\)

\(\Rightarrow A⋮13\)

Answer 4

Ta có : A = 3 + 3² + 3³ + ..... + 3²⁹ + 3³⁰

=> A = (3 + 3² + 3³) + (3⁴ + 3⁵ + 3⁶) + ...... + (3²⁸ + 3²⁹ + 3³⁰)

=> A = 3(1 + 3 + 3²) + 3⁴(1 + 3 + 3²) + ..... + 3²⁸(1 + 3 + 3²)

=> A = 3.13 + 3⁴.13 + ..... + 3²⁸.13

=> A = 13( 3 + 3⁴ + ..... + 3²⁸) chia hết cho 13