Question

Cho A=1+3+3²+…..+3¹¹ chứng tỏ A \(⋮\) 4

Answer 1

\(A=1+3+3^2+...+3^{11}\)

\(=\left(1+3\right)+\left(3^2+3^3\right)+...+\left(3^{10}+3^{11}\right)\)

\(=\left(1+3\right)+3^2\left(1+3\right)+...+3^{10}\left(1+3\right)\)

\(=4\left(1+3^2+...+3^{10}\right)⋮4\)

Answer 2

`#3107.101107`

`A = 1 + 3 + 3^2 + ... + 3^11`

`= (1 + 3) + (3^2 + 3^3) + ... + (3^10 + 3^11)`

`= (1 + 3) + 3^2(1 + 3) + ... + 3^10(1 + 3)`

`= (1 + 3)(1 + 3^2 + ... + 3^10)`

`= 4(1 + 3^2 + ... + 3^10)`

Vì `4(1 + 3^2 + ... + 3^10) \vdots 4`

`=> A \vdots 4.`