# Absolute Convergence

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.[1] 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 absolutely convergent.

### Example

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 , So converges absolutely.

### References

1. 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
2. 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
3. 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. http://www.allmathwords.org/en/c/convergent.html.

McAdams, David E. Absolute Convergence. 1/5/2019. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/a/absoluteconvergence.html.

### Revision History

1/5/2019: Corrected grammar. (McAdams, David E.)
12/21/2018: Reviewed and corrected IPA pronunication. (McAdams, David E.)
11/19/2008: Initial version. (McAdams, David E.)

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