Alternating Series

Pronunciation: /ˈɔl tərˌneɪ ting ˈsɪər iz/ ?

An alternating series is a series that alternates between negative and positive terms: [1]
The sum from n equals zero to infinity of negative 1 to the n times a sub n where a sub n > 0 for all n or a sub n < 0 for all n
An example of an alternating series is:
The sum from n equals zero to infinity of negative 1 to the n times 2 raised to the n equals 1 - 1/2 + 1/4 - 1/8 + ...

References

  1. alternating series. merriam-webster.com. Encyclopedia Britannica. (Accessed: 2009-03-12). http://www.merriam-webster.com/dictionary/alternating series.
  2. Introduction to Infinite Series, Chap. 1 sec. 11 pg 11. Osgood, William F., 1897. (Accessed: 2009-12-24). http://www.archive.org/stream/introductiontoi01osgogoog#page/n16/mode/1up/search/alternating.

More Information

  • Dawkins, Paul. Alternating Series Test. Lamar University. 2009-03-12. http://tutorial.math.lamar.edu/Classes/CalcII/AlternatingSeries.aspx.

Cite this article as:


Alternating Series. 2009-12-24. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/a/alternatingseries.html.

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Revision History


2009-12-25: Added "References" (McAdams, David.)
2008-11-25: Changed equations to images (McAdams, David.)
2008-11-20: Initial version (McAdams, David.)

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