Let $\sum_{n \geq 0} a_n z^n$ with radius of convergence $R >0$. Show that if all the $a_n$ are positive, then the point $z=R$ is singular.
I found that $\sum_{n \geq 0} a_n R^n \geq \min\{a_n : n \in \mathbb{N}\} \sum_{n \geq 0} R^n$. Is it a mistake of the book that $R$ have to be greater than $0$? I think $R$ have to be greater than $1$. Am I right?