Question

 Chứng minh: \(3^{n+2}-2^{n+2}+3^n-2^n\)chia hết cho 10

Answer 1

= 3ⁿ. 3² - 2ⁿ. 2² +3ⁿ -2ⁿ

⁼ 3ⁿ (3² + 1 ) - 2ⁿ ( 2² +1 )

= 3 ^{n .} 10  - 2ⁿ. 5 chia het cho 10

Answer 2

Cần thêm điều kiện  \(n\in\)N*

Answer 3

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

\(=\left(3^{n+2}+3^n\right)-\left(2^{n+2}-2^n\right)\)

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

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

\(=3^n.\left(3^2+1\right)-2^n.\left(2^2+1\right)\)

\(=\left(3^n.10\right)-\left(2^n.5\right)\)chia hết cho 10

Suy ra \(3^{n+2}-2^{n+2}+3^n-2^n\)chia hết cho 10