Question

chung minh rang :

36³⁶- 9¹⁰ se chia het cho 45

2 ¹⁰ + 2¹¹ +2¹² se chia het cho 7

81⁷- 27⁹- 9¹³ se chia het cho 45

3ⁿ⁺³+ 3 ⁿ⁺² +2ⁿ⁺³ +2ⁿ⁺² se chia het cho 6 moi n thuoc N

minh se tick cho nhung ai nhanh nhat va dung nhat nhe

Answer 1

Chứng minh rằng:

\(2^{10}+2^{11}+2^{12}\)

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

\(=2^{10}.7\) \(⋮\) 7

Vậy \(2^{10}+2^{11}+2^{12}\) chia hết cho 7

Answer 2

Chứng minh rằng:

\(3^{n+3}+3^{n+2}+2^{n+3}+2^{n+2}\)

\(=3^n.3^3+3^n.3^2+2^n.2^3+2^n.2^2\)

\(=3^n\left(3^3+3^2\right)+2^n\left(2^3+2^2\right)\)

\(=36.3^n+12.3^n\)

\(=6\left(6.3^n+2.3^n\right)\) \(⋮\) 6 với mọi n \(\in\) N

Vậy \(3^{n+3}+3^{n+2}+2^{n+3}+2^{n+2}\) chia hết cho 6 với mọi n \(\in\) N

Answer 3

Chứng minh rằng:

\(81^7-27^9-9^{13}\)

\(=\left(3^4\right)^7-\left(3^3\right)^9-\left(3^2\right)^{13}\)

\(=3^{28}-3^{27}-3^{26}\)

\(=3^{24}\left(3^4-3^3-3^2\right)\)

\(=3^{24}.45\) \(⋮\) 45

Vậy \(81^7-27^9-9^{13}\) chia hết cho 45