$\lim\limits_{n\to\infty} \dfrac{n!}{n^2} \rightarrow \lim\limits_{n\to\infty}\dfrac{\left(n-1\right)!}{n}$
I can understand that this will go to infinity because the numerator grows faster.
I am trying to apply L'Hôpital's rule to this; however, have not been able to figure out how to take the derivative of $\left(n-1\right)!$
So how does one take the derivative of a factorial?
Answer
you could introduce the gamma function!
Just a joke, as $n!>n^3$ for $n>100$ you know that
$$\frac{n!}{n^2} > \frac{n^3}{n^2}=n$$
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