Pronunciation: /dɪˈvɜr.dʒənt/ Explain

Most authors divide infinite series into two classes: convergent and divergent. A series is convergent if the sum of the series approaches a finite limit.

A series is divergent if it is not convergent.

Other authors divide infinite series into three classes: convergent, divergent and oscillating. An infinite series is convergent if it approaches a finite value, divergent if it approaches an infinite value[2], and oscillating if it does not approach any value.

An object that is divergent is said to diverge.

An example of an infinite series that diverges is the harmonic series:

Sum for n = 1 to infinity of 1/n: 1 + 1/2 + 1/3 + 1/4 + 1/5 + ....


  1. McAdams, David E.. All Math Words Dictionary, divergent. 2nd Classroom edition 20150108-4799968. pg 64. Life is a Story Problem LLC. January 8, 2015. Buy the book
  2. Hardy, G. H.. Divergent Series. pg 1. www.archive.org. Oxford. 1949. Last Accessed 7/3/2018. http://www.archive.org/stream/divergentseries033523mbp#page/n22/mode/1up. Buy the book
  3. Osgood, William F.. Introduction to Infinite Series. 3rd edition. pg 2. archive.org. Harvard University. 1910. Last Accessed 7/3/2018. http://www.archive.org/stream/introductiontoin00osgo#page/2/mode/1up/search/divergent. Buy the book
  4. Bromwich, T. J. I'a.. An Introduction to the Theory of Infinite Series. pg 2. www.archive.org. Macmillan and Company, Limited. 1908. Last Accessed 7/3/2018. http://www.archive.org/stream/introductiontoth00bromuoft#page/2/mode/1up/search/divergent. Buy the book

Cite this article as:

McAdams, David E. Divergent. 3/11/2019. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/d/divergent.html.

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Revision History

12/21/2018: Reviewed and corrected IPA pronunication. (McAdams, David E.)
7/4/2018: Removed broken links, updated license, implemented new markup, implemented new Geogebra protocol. (McAdams, David E.)
1/24/2010: Rewrote article. (McAdams, David E.)
11/22/2009: Added definition of to diverge. (McAdams, David E.)
12/13/2008: Initial version. (McAdams, David E.)

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