Radius of convergence of $\sum_{n=0}^{\infty} z^{n!}$? What is the radius of convergence of $\sum_{n=0}^{\infty} z^{n!}$?
I tried using ratio test and root test , applying the latter leaves me with the same type of problem again that is with  $\sum_{n=0}^{\infty} z^{(n-1)!}$ ?.

Hadamard's formula gives the answer at once: 
If $\sum_n a_n zn$ is a power series, its radius of convergence $R$ is given by
$$\frac1R=\limsup_{n\to\infty} \bigl(\lvert a_n\rvert^{1/n}\bigr)=1.$$
