By applying the root test on a power series \(\sum_{n=0}^{\infty} a_n(z-z_0)^n\) the radius of convergence is given by
\begin{equation*} r=\frac{1}{\limsup_{n \to \infty} \sqrt[n]{\lvert a_n\rvert}} . \end{equation*}If \(r=1/0\) we set \(r=\infty\).