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To find the radius of convergence $R$ of the series $\sum a_n x^n$ where $a_n = \frac{n!}{n^n}$, we use the root test: $$ \frac{1}{R} = \lim_{n \to \infty} |a_n|^{1/n}. _____ ______ _________ __________ ___ ______.
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