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Re: A bug?......In[1]:= Sum[Cos[x], {x, 0, Infinity, Pi}]......Out[1]= 1/2

• To: mathgroup at smc.vnet.net
• Subject: [mg41614] Re: [mg41594] A bug?......In[1]:= Sum[Cos[x], {x, 0, Infinity, Pi}]......Out[1]= 1/2
• From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
• Date: Thu, 29 May 2003 08:13:39 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

Sometimes what looks like a bug or  plain nonsense turns out to be 
simply a piece of more advanced mathematics than what you have been 
considering. (That's of course one of the nice things about mathematics 
:-) )
   The sum is indeed divergent in a conventional sense but there are 
other (perfectly rigorous) senses (one due to Abel) in which it can be 
summed to give precisely 1/2.

(However, whether it is right for it to do so in a student version is 
another matter.)

Andrzej Kozlowski
Yokohama, Japan
http://www.mimuw.edu.pl/~akoz/
http://platon.c.u-tokyo.ac.jp/andrzej/


On Wednesday, May 28, 2003, at 05:57  pm, Mark wrote:

> I think that the sum does not converge.  Does
> the following (from Mathematica for Students,
> v. 4.0.1) reveal a bug?  If so, do you have
> any insight into this bug?
>
>
>    In[1]:= Sum[Cos[x], {x, 0, Infinity, Pi}]
>
>    Out[1]= 1/2
>
>
>
>
>
> **********
> 1366294709
>
>
>

• Follow-Ups:
  • Re: Re: A bug?......In[1]:= Sum[Cos[x], {x, 0, Infinity, Pi}]......Out[1]= 1/2
    • From: Murray Eisenberg <murraye@attbi.com>