Question

 

Answer 1

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

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

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

\(=3^n\cdot10-2^n\cdot5\)

\(=10\cdot\left(3^n-\dfrac{2^n}{2}\right)\)

\(=10\cdot\left(3^n-2^{n-1}\right)\)

Mà: \(10\cdot\left(3^n-2^{n-1}\right)\) ⋮ \(n\forall n\)

\(\Rightarrow3^{n+2}-2^{n+2}+3^n-2^n\) ⋮ \(n\forall n\)

Answer 2

A=3^n*9+3^n-2^n*4-2^n

\(=10\cdot3^n-2^n\cdot5\)

\(=10\cdot\left(3^n-2^{n-1}\right)⋮10\)