Definition:Absolutely Convergent Series

Let $$\sum_{n=1}^\infty a_n$$ be a convergent series in a metric space.

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

A series which is convergent, but not absolutely convergent, is said to be conditionally convergent.