Pronunciation: /ˈæb.səˌlut kənˈvɜr.dʒəns/ Explain
A series is said to converge absolutely if the
sum of the absolute values of the
terms is convergent.
In algebraic notation: A series
is said to converge absolutely if .
A series that converges absolutely, also converges itself. If two absolutely
convergent series are multiplied together, the resulting series is also
Start with the series
If the series
converges, then the series is absolutely convergent. Since
is a infinite geometric series with a ratio of
it converges to
- McAdams, David E.. All Math Words Dictionary, absolute convergence. 2nd Classroom edition 20150108-4799968. pg 9. Life is a Story Problem LLC. January 8, 2015. Buy the book
- absolute convergence. merriam-webster.com. Encyclopedia Britannica. Merriam-Webster. Last Accessed 6/12/2018. https://www.merriam-webster.com/dictionary/absolute%20convergence. Buy the book
- Manning, Henry Parker, Ph.D.. Irrational Numbers and Their Representation by Series and Sequences. pg 89. www.archive.org. John Wiley & Sons. 1906. Last Accessed 6/12/2018. http://www.archive.org/stream/irrationalnumbe00manngoog#page/n100/mode/1up. Buy the book
- McAdams, David E.. Convergent. allmathwords.org. All Math Words Encyclopedia. Life is a Story Problem LLC. 6/19/2018. https://www.allmathwords.org/en/c/convergent.html.
- Conditional & absolute convergence. www.khanacademy.org. Kahn Academy. 6/19/2018. https://www.khanacademy.org/math/ap-calculus-bc/bc-series/bc-ratio-alt-series/v/conditional-and-absolute-convergence.
Cite this article as:
McAdams, David E. Absolute Convergence. 1/5/2019. All Math Words Encyclopedia. Life is a Story Problem LLC. https://www.allmathwords.org/en/a/absoluteconvergence.html.
1/5/2019: Corrected grammar. (McAdams, David E.)
12/21/2018: Reviewed and corrected IPA pronunication. (McAdams, David E.)
6/12/2018: Removed broken links, updated license, implemented new markup. (McAdams, David E.)
1/4/2010: Added "References". (McAdams, David E.)
11/19/2008: Initial version. (McAdams, David E.)