Asymptotic Proofs - BigOh/BigTheta This is not homework, but from a past exam. I do not know how to solve this one at all. Can anyone please take the time and show me how to do these? Thank you.


  Prove that $5^n \in O(6^n)$, but that $5^n \notin \Theta(6^n)$. (Doing this shows that $6^n$ bounds $5^n$ from above, but that $6^n$ is not the tightest such bound.)


I am familiar with the definitions, but it seems that $5^n$ is clearly $\lt 6^n$. and $5^n$ is not $\gt 6^n$.
Hint: Show that $$\lim_{n\to\infty} \frac{5^n}{6^n} = 0.$$