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MathGroup Archive 2003

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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]


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