Definition:Absolutely Convergent Series/Real Numbers

Definition
Let $\displaystyle \sum_{n \mathop = 1}^\infty a_n$ be a series in the real number field $\R$.

Then $\displaystyle \sum_{n \mathop = 1}^\infty a_n$ is said to be absolutely convergent iff:
 * $\displaystyle \sum_{n \mathop = 1}^\infty \left|{a_n}\right|$ is convergent

where $\left|{a_n}\right|$ denotes the absolute value of $a_n$.

Also see

 * Definition:Conditional Convergence, the antithesis of absolute convergence.