Hello,

I have some probelm regarding my homework.

I proved that the sequence $\displaystyle (-5)^{n}$ doesn't have limit and now I need to prove that the following sequence doesn't have limit too:

$\displaystyle \lim_{n \to \infty} \frac{(-5)^{n+1} + 5^n}{(-2)^n + 3}$

I tried to disprove it by the definition but it's doesn't go well so far, also I think it have to do something with the part that the sequence $\displaystyle (-5)^{n}$ doesn't have limit.

What is the best way to prove that this sequence doesn't have limit?

Thanks for your help.