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Power Serieseasy
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If a power series ∑n=0∞an(x−3)n\sum_{n=0}^{\infty} a_n (x-3)^n∑n=0∞​an​(x−3)n has radius of convergence R=5R = 5R=5, what is the radius of convergence for the series ∑n=0∞an(x−3)2n\sum_{n=0}^{\infty} a_n (x-3)^{2n}∑n=0∞​an​(x−3)2n?