Divergent geometric series
id:
divergent-geometric-series-185-12742992
title:
Divergent geometric series
text:
In mathematics, an infinite geometric series of the form
- ∑ n = 1 ∞ a r n − 1 = a + a r + a r 2 + a r 3 + ⋯ is divergent if and only if | r | > 1. Methods for summation of divergent series are sometimes useful, and usually evaluate divergent geometric series to a sum that agrees with the formula for the convergent case
- ∑ n = 1 ∞ a r n − 1 = a 1 − r. This is true of any summation method that possesses the properties of regularity, linearity, and stability.
brand slug:
wiki
category slug:
encyclopedia
description:
original url:
https://en.wikipedia.org/wiki/Divergent_geometric_series
date created:
2007-02-28T21:07:51Z
date modified:
2024-09-08T04:25:59Z
main entity:
{"identifier":"Q5283907","url":"https://www.wikidata.org/entity/Q5283907"}
image:
fields total:
13
integrity:
14