Question

URGENTA!!
Aratati ca:
a.
b.
c.

Answer 1

[tex]a)3\cdot 2^{n+2}-5\cdot 2^{n+1}+7\cdot 2^n \vdots 9\\ 3\cdot 2^n\cdot 4-5\cdot 2^n\cdot 2+7\cdot 2^n \vdots 9\\ 12\cdot 2^n-10\cdot 2^n+7\cdot 2^n\vdots 9\\ 2^n(12-10+7)\vdots 9\\ 2^n\cdot 9\vdots 9(A)\forall n\geq0,n\in \mathbb{N}\\[/tex]
[tex]b)3\cdot 4^{n+2}-5\cdot 2^{2n}\vdots 43\\ 3\cdot 4^n\cdot 16-5\cdot 4^n\vdots 43\\ 48\cdot 4^n-5\cdot 4^n\vdots 43\\ 4^n(48-5)\vdots 43\\ 4^n\cdot 43\vdots 43(A)\forall n \geq 0,n\in \mathbb{N}[/tex]
[tex]c)2^{2n+1}\cdot 5^{2n}+5^{2n+1}\cdot 2^{2n}\vdots 7\\ 4^{n}\cdot 2\cdot 25^n+25^n\cdot 5\cdot 4^n\vdots 7\\ 100^n(2+5)\vdots 7\\ 100^n\cdot 7\vdots 7(A)\forall n\geq 0,n\in \mathbb{N}[/tex]