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I was thinking about the problem that says: What is the radius of convergence of $\sum_{0}^{\infty}z^{n!}$ ?

Please help. Thanks everyone in advance for your time.

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    22 minutes. $ $2012-12-07

1 Answers 1

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You mean the radius of convergence of $\sum_{0}^{\infty}z^{n!}$

We have $a_{n!}=1$ for all $n!$. Then by Hadamard's theorem we have $\lim_{n=m!,n\rightarrow \infty}\sup (1)^{1/n}=1$

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    This is a good point. Thank you.2012-12-07