Prove that a power series$\sum_{n=0}^\infty a_nz^n$ which is convergent for any $ z \in \Bbb N$, converges for any $z \in \Bbb C$.
Prove that a power series $\sum_{n=0}^{\infty}{{a_n}{z^n}}$ which converges for any $z \in \mathbb{N}$, converges for any $z \in \mathbb{C}$.