Divergent
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:
.
References
- 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
- 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
- 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
- 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. https://www.allmathwords.org/en/d/divergent.html.
Image Credits
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.)