State Liouville's theorem on the approximation of algebraic numbers by rationals.

Suppose that we have a sequence $\zeta_{n}$ with $\zeta_{n} \in\{0,1\}$. State and prove a necessary and sufficient condition on the $\zeta_{n}$ for

$$\sum_{n=0}^{\infty} \zeta_{n} 10^{-n !}$$

to be transcendental.