Các bạn giúp mình nhé

\(S=\left(1+3\right)+...+3^8\left(1+3\right)=4\left(1+...+3^8\right)⋮4\)

\(S=\left(1+3+3^2\right)+...+3^7\left(1+3+3^2\right)\)

\(=13\left(1+...+3^7\right)⋮13\)

\(S=1+3+3^2+3^3+3^4+3^5+3^6+3^7+3^8+3^9\)

\(S=\left(1+3\right)+\left(3^2+3^3\right)+\left(3^4+3^5\right)+\left(3^6+3^7\right)+\left(3^8+3^9\right)\)

\(S=4+3^2\left(1+3\right)+3^4\left(1+3\right)+3^6\left(1+3\right)+3^8\left(1+3\right)\)

\(S=4+3^2.4+3^4.4+3^6.4+3^8.4\)

\(S=4\left(3^2+3^4+3^6+3^8\right)\)

\(4⋮4\\ \Rightarrow4\left(3^2+3^4+3^6+3^8\right)⋮4\\ \Rightarrow S⋮4\)

\(B=3+3^2+3^3+3^4+3^5+3^6+3^7+3^8\\=(3+3^2)+(3^3+3^4)+(3^5+3^6)+(3^7+3^8)\\=3\cdot(1+3)+3^3\cdot(1+3)+3^5\cdot(1+3)+3^7\cdot(1+3)\\=3\cdot4+3^3\cdot4+3^5\cdot4+3^7\cdot4\\=4\cdot(3+3^3+3^5+3^7)\)

Vì \(4\cdot(3+3^3+3^5+3^7) \vdots 4\)

nên \(B\vdots4\).

`#3107.101107`

\(B=3+3^2+3^3+3^4+3^5+3^6+3^7+3^8\)

\(=\left(3+3^2\right)+\left(3^3+3^4\right)+\left(3^5+3^6\right)+\left(3^7+3^8\right)\)

\(=3\left(1+3\right)+3^3\left(1+3\right)+3^5\left(1+3\right)+3^7\left(1+3\right)\)

\(=\left(1+3\right)\left(3+3^3+3^5+3^7\right)\)

\(=4\left(3+3^3+3^5+3^7\right)\)

Vì \(4\left(3^3+3^5+3^7\right)\) $\vdots 4$

`\Rightarrow B \vdots 4`

Vậy, `B \vdots 4.`

B=3+32+33+34+35+36+37+38=(3+32)+(33+34)+(35+36)+(37+38)=3⋅(1+3)+33⋅(1+3)+35⋅(1+3)+37⋅(1+3)=3⋅4+33⋅4+35⋅4+37⋅4=4⋅(3+33+35+37)

Vì 4⋅(3+33+35+37)⋮44⋅(3+33+35+37)⋮4

nên $B⋮4$.

\(S=1.\left(1+3\right)+3^2\left(1+3\right)+3^4\left(1+3\right)+...+3^8\left(1+3\right)\)

\(S=4x\left(1+3^2+...+3^8\right)\)

Vì 4 chia hết cho 4 nên S chia hết cho 4

Đặt A = 3² + 3³ + 3⁴ + ... + 3⁹⁹

= 3² + 3³ + (3⁴ + 3⁵ + 3⁶) + (3⁷ + 3⁸ + 3⁹) + ... + (3⁹⁷ + 3⁹⁸ + 3⁹⁹)

= 36 + 3⁴.(1 + 3 + 3²) + 3⁷.(1 + 3 + 3²) + ... + 3⁹⁷.(1 + 3 + 3²)

= 36 + 3⁴.13 + 3⁷.13 + ... + 3⁹⁷.13

= 36 + 13.(3⁴ + 3⁷ + ... + 3⁹⁷)

Do 36 không chia hết cho 13

13.(3⁴ + 3⁷ + ... + 3⁹⁷) ⋮ 13

⇒ 36 + 13.(3⁴ + 3⁷ + ... + 3⁹⁷) không chia hết cho 13

⇒ A không chia hết cho 13

Em xem lại đề nhé, có thể em viết thiếu số 3 rồi

`#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 \(A\vdots13\)

\(\text{#}Toru\)

\(3^{15}+3^{14}+3^{13}\)

\(=3^{13}\left(3^2+3+1\right)=3^{13}\cdot13⋮13\)

\(=3^{13}\left(3^2+3+1\right)=3^{13}\cdot13⋮13\)

\(3^{15}+3^{14}+3^{13}\)

\(=3^{13}\left(3^2+3+1\right)\)

\(=3^{13}\left(9+3+1\right)\)

\(=3^{13}.13\)⋮13

⇒\(3^{15}+3^{14}+3^{13}\)⋮13