Ononot — Let f(x) = \sum{n=0}^{\infty} cn x^n be a power series with

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Power Serieshard

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Let $f(x) = \sum_{n=0}^{\infty} c_n x^n$ be a power series with radius of convergence $R=2$ . Let $g(x) = \sum_{n=0}^{\infty} c_n x^{2n}$ . Which of the following is true about the radius of convergence $R_g$ of $g(x)$ ?