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This was an exam question which I wasn't sure how to solve:

Suppose [TEX]f[/TEX] is entire and [TEX]|f(z)| \leq C(1+ |z|)^n[/TEX] for all [TEX]z \in \mathbb{C}[/TEX] and for some [TEX]n \in \mathbb{N}[/TEX].

Prove that [TEX]f[/TEX] is a polynomial of degree less than or equal to [TEX]n[/TEX].

I know that f can be expressed as a power series, but I'm not sure how to show that the upper limit of the sum has to be less than or equal to n.

Thanks!