Let $f(z)=\sum_{n\geq 0}a_n z^n$ for $z\in D(0,1)$ and $|n!a_n|\leq M$ for all $n\geq 0$ and for some $M\geq 0$. Prove that $f$ is entire.
I feel that this question is missing some hypothesis. Perhaps $f$ is continuous on $\mathbb{C}$?
Edit: I was trying to ask a modified version of another question, but I made a simple mistake. The hypothesis is supposed to read $|n!a_n|\leq M$. In this case, I feel like this is an easy problem, but I'll ask again if I get stuck.