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Power Serieshard
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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=2R=2R=2. Let g(x)=∑n=0∞cnx2ng(x) = \sum_{n=0}^{\infty} c_n x^{2n}g(x)=∑n=0∞​cn​x2n. Which of the following is true about the radius of convergence RgR_gRg​ of g(x)g(x)g(x)?