The Cauchy-Hadamard Theorem provides a way to determine the radius of convergence for power series. It states that the radius of convergence, denoted as $R$, can be calculated using the formula $$\frac{1}{R} = \limsup_{n \to \infty} \sqrt[n]{|a_n|}$$, where $a_n$ are the coefficients of the power series. This theorem is essential in understanding the behavior of series, particularly when dealing with power series and Laurent series, as it helps in identifying where these series converge or diverge.
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