A series 
is said to converge
absolutely if the series 
converges,
where 
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.
Absolute Convergence
See also
Conditional Convergence, Convergent Series, Riemann Series TheoremExplore with Wolfram|Alpha
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.Jeffreys, H. and Jeffreys, B. S. "Absolute Convergence." §1.051 in Methods of Mathematical Physics, 3rd ed. Cambridge, England: Cambridge University Press, p. 16, 1988.Referenced on Wolfram|Alpha
Absolute ConvergenceCite this as:
Weisstein, Eric W. "Absolute Convergence." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/AbsoluteConvergence.html