# Thread: Prove that radius of convergence is at most 1

1. ## Prove that radius of convergence is at most 1

Hello,
I need some help starting a proof that asks the following.

Suppose that the coefficients of the power series [Summation of a_n * z^n] are integers, infinately many of which are disctinct from zero. Prove that the radius of convergence is at most 1.

This question is 10 in baby rudin's chapter 3.
Any help and hints as to how to start this problem will be greatly appreciated.

2. ## Re: Prove that radius of convergence is at most 1

If the radius of convergence is strictly greater than $1$, then the series converges at $1$ so the $a_n$ are $0$ for $n$ large enough.