Question

Cho S\(=\) 1\(+\)2\(+\)2²\(+\)2³\(+\)2⁴\(+\)2⁵\(+\)2⁶\(+\) 2⁷ . Chứng minh S \(⋮\)3

Answer 1

https://hoc247.net/hoi-dap/toan-6/chung-minh-s-1-2-2-2-2-3-2-4-2-5-2-6-2-7-chia-het-cho-3-faq250754.html

Answer 2

S= \(1+2+2^2+...+2^7\)

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

2S= \(2^1+2^2+...2^8\)

1S= 2S - S = \(\left(2^1+2^2+...2^8\right)-\left(1+2+2^2+...+2^7\right)\)

1S= \(2^1+2^2+...+2^8-1-2-2^2-...-2^7\)

1S= \(2^8-1\)

1S= \(256-1\)

1S= 255

=> 1S chia hết cho 3

Mà 1S= S

=> S chia hết cho 3

Vậy S chia hết cho 3

Answer 3

S$=$ 1 $+$ 2 $+$ 2² $+$ 2³ $+\; 24$$+$2⁵$+$ 2⁶$+$ 2⁷

S = (1 2) (2² 2³) 2⁵ (2⁶ 2⁷)

S = (1 2) 2² (1 2) 1 22⁶ (1 2)

S = 3 * 1 + 2² * 3 + 2⁴ * 33 + 2^{6 *} 33

S = 3 * ( 1 + 2² + 2⁴ + 2⁶ )

Vì 3 ⁝ 3

nên 3 * (1 + 2² + 2⁴ + 2⁶ ) ⁝ 3

Vậy S ⁝ 3