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Power Seriesmedium
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If f(x)=∑n=0∞anxnf(x) = \sum_{n=0}^{\infty} a_n x^nf(x)=∑n=0∞​an​xn has a radius of convergence RRR, what is the radius of convergence for the series ∑n=0∞anx2n\sum_{n=0}^{\infty} a_n x^{2n}∑n=0∞​an​x2n?