Divergent

Pronunciation: /dɪˈvɜrdʒənt/ ?

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. divergent. http://wordnet.princeton.edu/. WordNet. Princeton University. (Accessed: 2011-01-08). http://wordnetweb.princeton.edu/perl/webwn?s=divergent&sub=Search+WordNet&o2=&o0=1&o7=&o5=&o1=1&o6=&o4=&o3=&h=.
  2. diverge. http://wordnet.princeton.edu/. WordNet. Princeton University. (Accessed: 2011-01-08). http://wordnetweb.princeton.edu/perl/webwn?s=divergent&sub=Search+WordNet&o2=&o0=1&o7=&o5=&o1=1&o6=&o4=&o3=&h=.
  3. Hardy, G. H.. Divergent Series, pg 1. Oxford, 1949. (Accessed: 2010-01-24). http://www.archive.org/stream/divergentseries033523mbp#page/n22/mode/1up.
  4. Osgood, William F.. Introduction to Infinite Series, 3rd edition, pg 2. Harvard University, 1910. (Accessed: 2010-01-24). http://www.archive.org/stream/introductiontoin00osgo#page/2/mode/1up/search/divergent.
  5. Bromwich, T. J. I'a.. An Introduction to the Theory of Infinite Series, pg 2. Macmillan and Company, Limited, 1908. (Accessed: 2010-01-24). http://www.archive.org/stream/introductiontoth00bromuoft#page/2/mode/1up/search/divergent.

Printed Resources

Cite this article as:


Divergent. 2010-01-24. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/d/divergent.html.

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2010-01-24: Rewrote article (McAdams, David.)
2009-11-22: Added definition of to diverge. (McAdams, David.)
2008-12-13: Initial version (McAdams, David.)

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