I thought it had to be true for all values of n, but my friend is saying that "small n values are not representative of when the sequence converges so they don't have to be accounted for".
For context, the question is about proving the convergence of the sequence $$\frac{c^n}{n!}$$
The inequality my friend used with the squeeze theorem was
$$0\le \frac{c^n}{n!} \le \frac cn$$
It can be seen that if you substitute in numbers like c=3 and n=2 the inequality is false.
Due to the nature of $ n! $ and $ n^c$ your friend is correct, Generally through the convergence of a sequence has to be taken as the limit approaches infinity for the $ a_{n}$ as $ n \to \infty $