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

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Power Serieshard

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Let $f(x) = \sum_{n=0}^{\infty} a_n x^n$ be a power series with radius of convergence $R$ . If $\lim_{n \to \infty} |\frac{a_{n+1}}{a_n}| = L > 0$ , what is the radius of convergence of $\sum_{n=0}^{\infty} a_n^k x^n$ for a fixed integer $k \geq 1$ ?