# Homework Help: Taylor Series

1. Aug 1, 2010

### WannaBe22

1. The problem statement, all variables and given/known data
Let $$f(z)=\sum_{n=0}^{\infty} a_n z^n$$ be analytic at {z: |z|<R} and satisfies:
$$|f(z)| \leq M$$ for every |z|<R.
Let's define: d=the distance between the origin and the closest zero of f(z).

Prove: $$d \geq \frac{R|a_0|}{M+|a_0|}$$.

Hope you'll be able to help me

Thanks !

2. Relevant equations
3. The attempt at a solution
I've tried using Cauchy's Inequality... But it doesn't give anything new for $$a_0$$.
I've also tried isolating $$a_0$$ from this inequality, but it gives me nothing...

Hope someone will be able to help me