Re: two different results for Sum[Log[n]/n...

*To*: mathgroup at smc.vnet.net*Subject*: [mg44317] Re: two different results for Sum[Log[n]/n...*From*: "David W. Cantrell" <DWCantrell at sigmaxi.org>*Date*: Wed, 5 Nov 2003 10:00:42 -0500 (EST)*References*: <bo7pbp$alu$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

Tom Garcia <tgarcia-ng at NhOiSvPeAmMiTnHdX.org> wrote: > I have Mathematica 4.0.1 (oldish I know). Could someone please explain > the behaviour below --- different outputs to same input just because of > some other input in between. If it's a bug, is it fixed in more recent > version? Yes, it seems to be fixed. I was unable to replicate the behaviour in version 5.0. It claimed correctly, both before and after the intermediate calculation, that Sum[Log[n]/(n),{n,1,Infinity}] does not converge. David Cantrell > $ math > Mathematica 4.0 for Students: Linux Version > Copyright 1988-1999 Wolfram Research, Inc. > -- Motif graphics initialized -- > > In[1]:= Sum[Log[n]/(n),{n,1,Infinity}] > > Sum::div: Sum does not converge. > > Log[n] > Out[1]= Sum[------, {n, 1, Infinity}] > n > > In[2]:= Sum[Log[n]/(n^2),{n,1,Infinity}] > > Out[2]= -Zeta'[2] > > In[3]:= Sum[Log[n]/(n),{n,1,Infinity}] > > Out[3]= -StieltjesGamma[1]