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

Tom Garcia <tgarcia-ng at> 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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