`#3107.101107`

\(A=1+3+3^2+3^3+...+3^{101}\)

$A = (1 + 3 + 3^2) + (3^3 + 3^4 + 3^5) + ... + (3^{99} + 3^{100} + 3^{101}$

$A = (1 + 3 + 3^2) + 3^3 (1 + 3 + 3^2)  + ... + 3^{99}(1 + 3 + 3^2)$

$A = (1 + 3 + 3^2)(1 + 3^3 + ... + 3^{99})$

$A = 13(1 + 3^3 + ... + 3^{99})$

Vì `13(1 + 3^3 + ... + 3^{99}) \vdots 13`

`\Rightarrow A \vdots 13`

Vậy, `A \vdots 13.`

\(A=1+3+3^2+3^3+3^4+3^5+...+3^{101}\\=(1+3+3^2)+(3^3+3^4+3^5)+(3^6+3^7+3^8)+...+(3^{99}+3^{100}+3^{101})\\=13+3^3\cdot(1+3+3^2)+3^6\cdot(1+3+3^2)+...+3^{99}\cdot(1+3+3^2)\\=13+3^3\cdot13+3^6\cdot13+...+3^{99}\cdot13\\=13\cdot(1+3^3+3^6+...+3^{99})\)

Vì \(13\cdot(1+3^3+3^6...+3^{99}\vdots13\)

nên \(A\vdots13\)

\(\text{#}Toru\)

2n+5 : 7
=>2n+5+7: 7
=> 2n+12:7
       2 (n+6):7
             n+6:7( UCLN 2,7=10
              n+6 =7k
               n=7k-1
Vậy n khác 7k-1  thì 2n+5:7 

đúng 100%

(n + 13) ⋮ 11

⇒ n + 13 ∈ B(11) = {0; 11; 22; 33; ...}

⇒ n ∈ {-13; -2; 9; 20; ...}

6 - (5 - 5847) + 5 - 5847

= 6 - 5 + 5847 + 5 - 5847

= 6 + (-5 + 5) + (5847 - 5847)

= 6

đáp án băng 1 á bạn

150 = 2.3.5²

315 = 3².5.7

ƯCLN(150; 315) = 3.5 = 15

Tính hợp lí:

13579 - (14-53) + (-13579)

= 13579 + ( - 13579) - (14 - 53)

= 39