Question

Giúp mình nha mình tick cho:

CMR: 3ⁿ⁺² + 3ⁿ - 2ⁿ⁺² -2ⁿ chia hết cho 10

Answer 1

Ta có:

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

= \(3^n.3^2+3^n-2^n.2^2-2^n\)

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

= \(3^n.10-2^n.5\)

= \(3^n.10-2^{n-1}.10\) = \(\left(3^n-2^{n-1}\right).10\)   => chia hết cho 10

Nhớ cho mk nha bạn !

Answer 2

Ta có 3^n+2+3^n-2^n+2-2^n

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

=3^n.(3^2+1)-2^n.(2^2+1)

=3^n.10-2^n.10

=3^n.10-2^(n-1).10=10.(3^n-2^(n-1)) chia hết cho 10(đpcm)