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Power Serieshard
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Let f(x)=∑n=0∞anxnf(x) = \sum_{n=0}^{\infty} a_n x^nf(x)=∑n=0∞​an​xn be a power series with radius of convergence RRR. If lim⁡n→∞∣an+1an∣=L>0\lim_{n \to \infty} |\frac{a_{n+1}}{a_n}| = L > 0limn→∞​∣an​an+1​​∣=L>0, what is the radius of convergence of ∑n=0∞ankxn\sum_{n=0}^{\infty} a_n^k x^n∑n=0∞​ank​xn for a fixed integer k≥1k \geq 1k≥1?