Category:Examples of Use of Abel's Limit Theorem

This category contains examples of use of Abel's Limit Theorem.

Let $\ds \sum_{k \mathop = 0}^\infty a_k$ be a convergent series in $\R$.

Then:

$\ds \lim_{x \mathop \to 1^-} \paren {\sum_{k \mathop = 0}^\infty a_k x^k} = \sum_{k \mathop = 0}^\infty a_k$

where $\ds \lim_{x \mathop \to 1^-}$ denotes the limit from the left.