Definition:Absolutely Convergent Series/Real Numbers

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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 absolutely convergent if and only if:

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

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


Also see


Sources