Date: Jan 26, 2013 8:52 AM
Author: A N Niel
Subject: Re: Series Convergence

In article <2013012613252172156-bpa2@mecom>, Barry <bpa2@me.com> wrote:> I have come to a complete dead stop with the following question:> > Find all real numbers $x$ such that the series> > > $> \sum_{n=1}^{\infty}\frac{x^n-1}{n}>$> converges.> > I am aware that> > $> \sum_{n=1}^{\infty}\frac{x^n}{n}=-\log(1-x)>$> and that> $> \sum_{n=1}^{\infty}\frac{1}{n}>$> does not converge.> > Any guidance on how to proceed would be much appreciated by this hobby > student (not on a formal course).> If $x>1$ or $x <= -1$ the term does not go to zero ... DIVERGE.If $-1 < x < 1$, compare to $\sum (-1/n)$ .... DIVERGE.IF $x=1$, all terms zero ... CONVERGE.