Radius of convergence of $\sum_{n=0}^\infty \frac{a_n}{c^n} x^n$ where $c\in\Bbb Z$ is a non-zero constant

Question

So I have a power series $\sum_{n=0}^\infty a_nx^n$ with radius of convergence $R=1$. I then want to find the radius of convergence of $\sum_{n=0}^\infty \frac{a_n}{c^n} x^n$ where $c$ is a non-zero constant in $\mathbb R$.

How can I start going about this?

Answer 1

Hint: you know that the series converges for $\left| \frac zc \right|<R$ and diverges for $\left| \frac zc \right|>R$.

Answer 2

Write the sum as $$\sum_{n=0}^\infty a_n\Bigl(\frac xc\Bigr)^n$$ Can you see it from this?