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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