\text { If } a_{n} \text { is a convergent sequence of positive numbers such that } f(x)=\sum_{n=0}^{\infty} a_{n} x^{n} \text { has radius of } \text { convergence } R \in(0, \infty) \text {, then determine the radius of convergence of } g(x)=\sum_{k=0}^{\infty} a_{3 k} x^{4 k}

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