Pringsheim's Theorem

Theorem
Let $f$ be a holomorphic function defined on a unit disc centered at the origin of the complex plane and is denoted by its Taylor series:
 * $\map f z = \ds \sum_{n \mathop = 0}^{\infty} c_n z^n$

Let:
 * $(1): \quad \forall n \ge 0: c_n \ge 0$
 * $(2): \quad$ the radius of convergence of the Taylor series of function $f$ is $1$.

Then $z = 1$ is an isolated singularity of $f$.