lean_workbook_plus_1011

Let $f(x)=\sum_{k=0}^{\infty}a_{k}x^{k}$ be a power series ( $a_{k}\in \mathbb{R}$ ). Suppose that $f(x)$ converges at $c$ where $c>0$ . Show that $f(x)$ converges at any $x$ with $|x|<c$ .