Category:Absolute Convergence

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This category contains results about Absolute Convergence.
Definitions specific to this category can be found in Definitions/Absolute Convergence.

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 absolutely convergent if and only if:

$\displaystyle \sum_{n \mathop = 1}^\infty \left|{a_n}\right|$ is convergent

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