> [!NOTE] Corollary (Absolute Series) > Let $\sum a_{n}x^{n}$ be a [[Power Series|univariate real power series about zero]] with [[Radius of Convergence of Complex Power Series|radius of convergence]] $R$. Then $\sum |a_{n}| x^{n}$ also has radius of convergence $R$. **Proof**: Follows directly from [[Radius of Convergence of Complex Power Series]].