Abels_Theorem

Let $\displaystyle \sum_{k \mathop = 0}^\infty a_k$ be a convergent series in $\R$. Then $\displaystyle \lim_{x \mathop \to 1^-} \paren {\sum_{k \mathop = 0}^\infty a_k x^k} = \sum_{k \mathop = 0}^\infty a_k$ where $\displaystyle \lim_{x \mathop \to 1^-}$ denotes the limit from the left.