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Re: Sum

  • To: mathgroup at
  • Subject: [mg55210] Re: Sum
  • From: dh <dh at>
  • Date: Thu, 17 Mar 2005 03:28:29 -0500 (EST)
  • References: <d192qe$ng4$>
  • Sender: owner-wri-mathgroup at

Hi mjumbo,
Auxilliary variables like k in Sum[..,{k,..}] are handled apart from 
ordinary variables. Otherwise the following example would give an error:
Mathematica does this by taking the unevaluated expression in: 
Sum[expr,{k,1,2}] and literally replace all "external" k against 
"internal" k's. In your casae it takes x (there is nothing to replace). 
Then it calculates the Sum, giving x times Infinity, then it replaces x 
by Exp[-k] giving Exp[-k] times Infinity.
If you want Mathematica to evaulate x first before replacing variables, 
you have to tell Mathematica by:

Sum[ Evaluate[x] ,{k,0,Infinity}]


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? It is rather vexing to copy/paste long expressions instead of using short placeholders like x.
> __________
> -- Íîâàÿ Ïî÷òà: âñå ïî-íîâîìó.

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