Question

b, CMR : Với mọi số nguyên dương n thì :
3ⁿ⁺² - 2ⁿ⁺² + 3ⁿ - 2ⁿ \(⋮\) 10

Answer 1

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

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

\(=2^n.9+2^n.4+3^n-2^n\)

\(=3^n\left(9+1\right)-2^n\left(4+1\right)\)

\(=3^n.10-2^n.5\)

\(=3^n.10-2^{n-1}.10\)

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