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
 * $f \left( z \right) = \displaystyle\sum_{n=0}^{\infty} c_n z^n$.

The theorem states that if $c_n \geq 0, \forall n \geq 0$ and the radius of convergence of the taylor series of function $f$ is 1, then $z = 1$ is a singular point of $f$.