Let $R$ be radius of convergence for $\sum^{\infty}_{n=0} a_n z^n$. find radius of convergence for $\sum^{\infty}_{n=0} a_n z^{kn+l}$ in terms of $R$.

score 91 · Answer 11 · 2014-05-14 10:19:14

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Use power series $\sum^{\infty}_{n=1} \frac {z^{n+1}} {n(n+1)}$ to show $\sum^{\infty}_{n=1} \frac {1} {n(n+1)} =1$.

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score 93 · Answer 12 · 2014-05-15 10:49:22

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score 176 · Answer 15 · 2014-05-17 07:45:57

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Let $R$ be radius of convergence for $\sum^{\infty}_{n=0} a_n z^n$. find radius of convergence for $\sum^{\infty}_{n=0} a_n z^{kn+l}$ in terms of $R$.

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