$\sum_{n=1}^{\infty} a^{-n!}$ is transcendental ??

Question

Is $\sum_{n=1}^\infty a^{-n !}$ transcendental for any positive integer a ?

I know $\epsilon =\sum_{n=1}^{\infty} 10^{-n!}$ is transcendental, for Liouville´s Theorem, ($p_k=10^{k!} \sum_{n=1}^k 10^{-n!}$ and $q_k=10^{k!}$. Then $| \epsilon -\frac{p_k}{q_k}| < q_k^{-k}.$ )