Show that $\lim_{n\to\infty}\frac{n}{(\log n)^2}=\infty$

Question

I am working on an asymptotic analysis question from a data structures past paper, and I need to show that $$\lim\limits_{n\to\infty}\frac{n}{(\log n)^2}=\infty$$

Could I have a hint for working out how to show this, please?

Answer 1

Hint: Use L'hopital's rule on the limit since it's in an indeterminate form.

Answer 2

note that $ log(n) \leq n^\alpha $ for any $\alpha >0$ for instance chose $\alpha = 1/4$ now apply comparison test

Alter: Use L'Hospitals Rule

Answer 3

Hint: $$\frac{\sqrt n}{\log n}\to +\infty \implies \frac{n}{(\log n)^2} \to +\infty$$ And you can have many ways to prove the first part.