Alternating Series

Pronunciation: /ˈɔl tərˌneɪ ting ˈsɪər iz/ Explain

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. Merriam-Webster. Last Accessed 8/6/2018. http://www.merriam-webster.com/dictionary/alternating series.
  2. Osgood, William F.. Introduction to Infinite Series. Chap. 1 sec. 11 pg 11. archive.org. Last Accessed 8/6/2018. http://www.archive.org/stream/introductiontoi01osgogoog#page/n16/mode/1up/search/alternating. Buy the book

More Information

  • Dawkins, Paul. Alternating Series Test. tutorial.math.lamar.edu. Lamar University. 6/19/2018. http://tutorial.math.lamar.edu/Classes/CalcII/AlternatingSeries.aspx.

Cite this article as:

McAdams, David E. Alternating Series. 6/13/2018. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/a/alternatingseries.html.

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Revision History

6/13/2018: Removed broken links, updated license, implemented new markup. (McAdams, David E.)
12/25/2009: Added "References". (McAdams, David E.)
11/25/2008: Changed equations to images. (McAdams, David E.)
11/20/2008: Initial version. (McAdams, David E.)

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