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Power Seriesmedium
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Let f(x)=∑n=0∞cnxnf(x) = \sum_{n=0}^{\infty} c_n x^nf(x)=∑n=0∞​cn​xn be a power series with radius of convergence R=5R=5R=5. What is the radius of convergence of the series ∑n=0∞cnx2n\sum_{n=0}^{\infty} c_n x^{2n}∑n=0∞​cn​x2n?