Absolute Convergence

A Series $\sum_n u_n$ is said to Converge absolutely if the Series $\sum_n \vert u_n\vert$ Converges, where $\vert u_n\vert$ denotes the Absolute Value. If a Series is absolutely convergent, then the sum is independent of the order in which terms are summed. Furthermore, if the Series is multiplied by another absolutely convergent series, the product series will also converge absolutely.

See also Conditional Convergence, Convergent Series, Riemann Series Theorem

References

Bromwich, T. J. I'a and MacRobert, T. M. ``Absolute Convergence.'' Ch. 4 in An Introduction to the Theory of Infinite Series, 3rd ed. New York: Chelsea, pp. 69-77, 1991.