example of ratio test

Consider the sequence given by an=xn (geometric progression) where |x|<1. Then the series


converges.  To see this, we can use the ratio testMathworldPlanetmath. We need to consider the sequence |an+1/an|. But for any  n0  we have (when  x0)


and therefore the series converges. The ratio test and the previous argument shows that the geometric seriesMathworldPlanetmath diverges for  |x|>1.

Title example of ratio test
Canonical name ExampleOfRatioTest
Date of creation 2013-03-22 15:03:20
Last modified on 2013-03-22 15:03:20
Owner drini (3)
Last modified by drini (3)
Numerical id 9
Author drini (3)
Entry type Example
Classification msc 26A06
Classification msc 40A05