Question

[nguyễn ngọc linh]

 Cho S = 3 + 3² + 3³ + ... + 3⁹ Chứng tỏ rằng S⋮13

Answer 1

[Doanh Bùi Xuân]

S = ( 3 + 3² +3³)+(3⁴+3⁵+3⁶) + (3⁷+3⁸+3⁹)

S = 3.(1+3+9)+3⁴.(1+3+9)+3⁷.(1+3+9)

S = 3.13 + 3⁴.13+3⁷.13

S = 13.(3+3⁴+3⁷) ⋮13 ( đpcm)

Tick cho mình

Answer 2

[『Kuroba ム Tsuki Ryoo ︵²ᵏ⁷』]

`#3107.101107`

`S = 3 + 3^2 + 3^3 + ... + 3^9`

`= (3 + 3^2 + 3^3) + ... + (3^7 + 3^8 + 3^9)`

`= 3(1 + 3 + 3^2) + ... + 3^7(1 + 3 +3^2)`

`= (1 + 3 + 3^2)(3 + ... + 3^7)`

`= 13(3 + ... + 3^7)` $\vdots 13$

$\Rightarrow S \vdots 13.$