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MathGroup Archive 2005

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Re: Sum

  • To: mathgroup at smc.vnet.net
  • Subject: [mg55256] Re: Sum
  • From: Bill Rowe <readnewsciv at earthlink.net>
  • Date: Thu, 17 Mar 2005 03:30:52 -0500 (EST)
  • Sender: owner-wri-mathgroup at wolfram.com

On 3/16/05 at 5:35 AM, mjumbo at nm.ru (mjumbo) wrote:

>Can sombody explain me why

>Sum[Exp[- k], {k, 0, Infinity}]

>gives the correct result, while the following (imho equivalent)
>statements

>x = Exp[-k]
>Sum[x, {k, 0, Infinity}]

>don't? What should I do to make it work? 

Use any of

x[k_]:= Exp[-k]
Sum[x[k], {k, 0, Infinity}]

x[k_]= Exp[-k]
Sum[x[k], {k, 0, Infinity}]

x = Exp[-k]
Sum[Evaluate[x], {k, 0, Infinity}]

The difference is when things get evaluated. With you syntax, x is not evaluated before the summation begins. You syntax is equivalent to Sum[y, {k, 0, Infinity}]/.y->Exp[-k]. That is the sum evaluatest to x Infinity then x gets evaluated for a result of Exp[-k] Infinity.
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