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Power Serieshard
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Suppose the coefficients ana_nan​ of f(x)=∑n=0∞anxnf(x) = \sum_{n=0}^{\infty} a_n x^nf(x)=∑n=0∞​an​xn satisfy lim sup⁡n→∞∣an∣1/n=12\limsup_{n \to \infty} |a_n|^{1/n} = \frac{1}{2}limsupn→∞​∣an​∣1/n=21​

What is the radius of convergence?