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.
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.
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 $\lim_{n=m!,n\rightarrow \infty}\sup (1)^{1/n}=1$