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:
.
References
- 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=.
- 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=.
- Hardy, G. H.. Divergent Series, pg 1. Oxford, 1949. (Accessed: 2010-01-24). http://www.archive.org/stream/divergentseries033523mbp#page/n22/mode/1up.
- 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.
- 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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Revision History
2010-01-24: Rewrote article (
McAdams, David.)
2009-11-22: Added definition of to diverge. (
McAdams, David.)
2008-12-13: Initial version (
McAdams, David.)