Answer
by ratio test the series is divergent for $x\ne a$ which gives us that the radius of the power series is $0=c$
Work Step by Step
If $c=0$ we have that $\lim\limits_{n \to \infty}|\frac{c_{n+1}}{c_{n}}|=+\infty$
Hence, we have that $\lim\limits_{n \to \infty}|\frac{a_{n+1}}{a_{n}}|=\lim\limits_{n \to \infty}(|\frac{c_{n+1}}{c_{n}}|x-a|)=0$ if $x=a$ and $\lim\limits_{n \to \infty}|\frac{a_{n+1}}{a_{n}}|=\lim\limits_{n \to \infty}(|\frac{c_{n+1}}{c_{n}}|x-a|)=+\infty$ if $x\ne a$.
Thus , we have by ratio test the series is divergent for $x\ne a$ which gives us that the radius of the power series is $0=c$
