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MathGroup Archive 2004

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Re: infinite sum problem

  • To: mathgroup at smc.vnet.net
  • Subject: [mg53005] Re: infinite sum problem
  • From: Bill Rowe <readnewsciv at earthlink.net>
  • Date: Sun, 19 Dec 2004 06:14:57 -0500 (EST)
  • Sender: owner-wri-mathgroup at wolfram.com

On 12/18/04 at 4:00 AM, m9085.NOSPAM at yahoo.com (marc) wrote:

>the following sum converges only for x<1, but Mathematica gives a
>result for general x when the sum is evaluated symbolically.

>In[1]:= Sum[(-1)^k*x^(2k),{k,0,Infinity}]

>Out[1]= \!\(1\/\(1 + x\^2\)\)

What version are you using? I get

$Version
"5.0 for Mac OS X (June 10, 2003)"

Sum[(-1)^k*x^(2*k), {k, 0, Infinity}]
Infinity
Sum::"div":"Sum does not converge. 
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