Question

CMR với mọi số nguyên dương n thì

3n+2-2n+2+3n-2n \(⋮\)10

Answer 1

Ta có :

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

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

=\(3^n.10-2^n.5=3^n.10-2^{n-1}.2.5\) = \(3^n.10-2^{n-1}.10\)

=\(10.\left(3^n-2^{n-1}\right)⋮10\)

\(\Rightarrow3^{n+2}-2^{n+2}+3^n-2^n⋮10\) (ĐPCM)

Answer 2

Sửa : 3ⁿ⁺²-2ⁿ⁺²+3ⁿ-2ⁿ

= 3ⁿ.9 - 2ⁿ.4+3ⁿ-2ⁿ

= 3ⁿ.10 - 2ⁿ.5

= 3ⁿ.10 - 2ⁿ.1/2.10

= 10 . (3ⁿ-2ⁿ.1/2) chia hết cho 10

Answer 3

mũ chớ

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