Prove by definition of limit $\displaystyle\lim_{n\to\infty} \dfrac{1}{n!} = 0$
I have no idea how to proceed with this. Usually I start with a preliminary computation and solve for $n$ in terms of $\epsilon$ from the definition of the limit:
$|\dfrac{1}{n!} - 0| < \epsilon$
Here, I do not see an approach to solve for n.

You can either try to find a $n$ for which 
$$
n!\geq \frac{1}{\epsilon}
$$
or as Brian suggested, you only need to find $n$ such that
$$
n\geq \frac{1}{\epsilon}.
$$
In either case, it proves that the limit goes to $0$.
