0x6725b195

Given a power series \(\sum_{n=0}^{\infty} a_n(z-z_0)^n\). If the limit of \(\lvert \frac{a_n}{a_{n+1}}\rvert\) exists, we obtain the radius of convergence by applying the ratio test which is given by

\begin{equation*} r= \lim_{n \to \infty}\lvert \frac{a_n}{a_{n+1}}\rvert \end{equation*}

The limit \(r=\infty\) is allowed.