Cauchy’s root test

If an is a series of positive real terms and


for all n>N, then an is convergentMathworldPlanetmath. If ann1 for an infinite number of values of n, then an is divergent.

Limit form

Given a series an of complex terms, set

ρ=lim supn|an|n

The series an is absolutely convergent if ρ<1 and is divergent if ρ>1. If ρ=1, then the test is inconclusive.

Title Cauchy’s root test
Canonical name CauchysRootTest
Date of creation 2013-03-22 12:58:03
Last modified on 2013-03-22 12:58:03
Owner Mathprof (13753)
Last modified by Mathprof (13753)
Numerical id 9
Author Mathprof (13753)
Entry type Theorem
Classification msc 40A05
Synonym root test
Related topic LambertSeries