I would be glad to get some help with this question:
Let $f(z)$ be an entire function. Assume that there exists a monotonous increasing and unbounded sequence $\{r_n\}$ such that $\lim\limits_{n \to \infty} \min\limits_{|z|=r_n} |f(z)|=\infty$. I want to show that there exists a $z_0 \in \mathbb C$ that satisfies $f(z_0)=0$.
I'd especially like to know how to use that fact about the sequence.
Thanks.