The Cauchy-Hadamard Theorem provides a formula to determine the radius of convergence for power series, which is a type of series where each term is a power of a variable multiplied by a coefficient. This theorem states that the radius of convergence can be found using the formula $$R = \frac{1}{\limsup_{n \to \infty} \sqrt[n]{|a_n|}}$$, where $R$ is the radius of convergence and $a_n$ are the coefficients of the power series. Understanding this theorem helps in identifying the intervals within which the power series converges absolutely, thus playing a crucial role in the study of power series and their properties.
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