The Harmonic Series and the nth Term Test for Divergence
History and Overview
2007-06-19 v1
Abstract
The divergence of the harmonic series is proved by direct comparison with a series whose nth partial sum telescopes to the natural logarithm of n. The key idea is to apply the classical inequality x>=log(1+x) (valid for x>-1) with x=1/k and sum over k, 1<=k<=n-1.
Keywords
Cite
@article{arxiv.0706.2513,
title = {The Harmonic Series and the nth Term Test for Divergence},
author = {David M. Bradley},
journal= {arXiv preprint arXiv:0706.2513},
year = {2007}
}