Divergent

Pronunciation: /dɪˈvɜrdʒənt/ 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, 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 + ....

References

  1. Hardy, G. H.. Divergent Series. pg 1. www.archive.org. Oxford. 1949. Last Accessed 8/6/2018. http://www.archive.org/stream/divergentseries033523mbp#page/n22/mode/1up. Buy the book
  2. Osgood, William F.. Introduction to Infinite Series. 3rd edition. pg 2. archive.org. Harvard University. 1910. Last Accessed 8/6/2018. http://www.archive.org/stream/introductiontoin00osgo#page/2/mode/1up/search/divergent. Buy the book
  3. 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 8/6/2018. http://www.archive.org/stream/introductiontoth00bromuoft#page/2/mode/1up/search/divergent. Buy the book

Cite this article as:

McAdams, David E. Divergent. 7/4/2018. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/d/divergent.html.

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Revision History

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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