Question

Vă rog să mă ajutați.E urgent.

Answer 1

O sa incep cu b:

b) 
$x = \frac{5^{n}(3^{n+1}+3^{n+2}+3^{n+3})}{5^{n}(2^{n}+2^{n+2}+2^{n+3})}$

$x=\frac{3^{n+1}+3^{n+2}+3^{n+3}}{2^{n}+2^{n+2}+2^{n+3}}$

$x=\frac{3^{n+1}(1+3+3^{2})}{2^n(1+2^{2}+2^{3})}$

$x=\frac{3^{n+1}}{2^n}\cdot\frac{13}{13} = \frac{3^{n+1}}{2^n}$

a)

$n^0=1,\:\forall n\in \mathbb{N}^{+}\implies$ 

$\implies\:x=\frac{3}{1}=3$