I have calculated using the root test that the radius of convergence of $\displaystyle\sum_{n=0}^\infty z^{n!}$ is $1$.
But how would I show that there is an infinite number of $z \in \mathbb{C}$ with $|z|=1$ for which the series diverge? I don't really understand what is meant in the above question, could someone explain to me what the question means?