Category:Definitions/Absolute Convergence

This category contains definitions related to Absolute Convergence.
Related results can be found in Category:Absolute Convergence.

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

Then $\ds \sum_{n \mathop = 1}^\infty a_n$ is absolutely convergent if and only if:

$\ds \sum_{n \mathop = 1}^\infty \size {a_n}$ is convergent

where $\size {a_n}$ denotes the absolute value of $a_n$.