Radius of convergence of this complex-numbers power series

Asked Jun 22 '20 at 14:16

Active Jun 22 '20 at 14:16

Viewed 20 times

I would like to calculate the radius of convergence of power series:

f(z)=\sum{n=0}^∞ n!z^(n!)

My mathematics book says that I can calculate it with Cauchy's test (limsup[n→∞] |a_n|^(1/n)).

However, I don't know what to do in order to calculate it.

I would like you to teach me how to calculate it.

asked Jun 22 '20 at 14:16

daㅤ

You could instead find $\lim_{n\to\infty}|a_{n+1}|/|a_n|$. See also this question. – Peter Foreman Jun 22 '20 at 14:23
If $z=1$ then divergence is obvious. If $z < 1$ ? – reuns Jun 22 '20 at 15:17

0 Answers0