This does not converhe for any . The proof hinges on showing that as . Then the limit of the terms does not go to zero, and so the series cannot converge.

A proof that as can be constructed by supposing otherwise, that is we suppose (for fixed ) that:

as .

This means that for all there exists an such that for all :

Now:

but by making sufficiently small we can make the right hand side of the last equation as close to as we like for , but this contradicts the consequence of our assumption that for sufficently small

UNDER CONSTRUCTION