proof of Cauchy’s root test

If for all nN




Since i=Nki converges so does i=Nan by the comparison testMathworldPlanetmath. If ann>1 then by comparison with i=N1 the series is divergent. Absolute convergence in case of nonpositive an can be proven in exactly the same way using |an|n.

Title proof of Cauchy’s root testMathworldPlanetmath
Canonical name ProofOfCauchysRootTest
Date of creation 2013-03-22 13:23:43
Last modified on 2013-03-22 13:23:43
Owner mathwizard (128)
Last modified by mathwizard (128)
Numerical id 5
Author mathwizard (128)
Entry type Proof
Classification msc 40A05