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Power Serieshard
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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 radius of convergence R=2R=2R=2, what is the radius of convergence of ∑n=0∞an2x2n\sum_{n=0}^{\infty} a_n^2 x^{2n}∑n=0∞​an2​x2n?