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

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  • Subject: [mg41835] Re: A bug?......In[1]:= Sum[Cos[x], {x, 0, Infinity, Pi}]......Out[1]= 1/2
  • From: Paul Abbott <paul at physics.uwa.edu.au>
  • Date: Fri, 6 Jun 2003 09:51:11 -0400 (EDT)
  • Organization: The University of Western Australia
  • References: <bbnaun$2eo$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

"Mark" <nanoburst at yahoo.com> 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

Interestingly, 

   Sum[Cos[x], {x, 0, Infinity, Pi}]

   1/2

but, the equivalent sum,

   Sum[Cos[n Pi], {n, 0, Infinity}]

   Sum::div: Sum does not converge.

However, 

   Sum[Cos[n Pi] t^n, {n, 0, Infinity}]

   1/(t + 1)

which yields 1/2 in the limit t->1.

Cheers,
Paul

-- 
Paul Abbott                                   Phone: +61 8 9380 2734
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