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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 S=∑n=0∞cnx3nS = \sum_{n=0}^{\infty} c_n x^{3n}S=∑n=0∞​cn​x3n. What is the radius of convergence of SSS?