radius of convergence of the power series $\sum_{n=0}^{\infty} z^{n!}$

Question

How to find the radius of convergence of the power series $$\sum_{n=0}^{\infty} z^{n!}?$$

I don't know how to start !!!

Do you know the Cauchy-Hadamard formula? – Daniel Fischer Dec 06 '13 at 13:20 — Daniel Fischer, Dec 06 '13 at 13:20

MichalisN · Accepted Answer · 2013-12-06T13:35:55.677

6

Hint: If $|z|<1$, $|z|^{n!}\leq|z|^n$, if $|z|>1$ $|z|^{n!}\geq|z|^n$.

edited Dec 06 '13 at 13:35

answered Dec 06 '13 at 13:21

MichalisN

1 Answers1