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Re: error with Sum and Infinity

  • To: mathgroup at smc.vnet.net
  • Subject: [mg102250] Re: [mg102245] error with Sum and Infinity
  • From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
  • Date: Mon, 3 Aug 2009 05:44:19 -0400 (EDT)
  • References: <200908021001.GAA01730@smc.vnet.net>

On 2 Aug 2009, at 19:01, Llewlyn wrote:

> Hi experts,
>
> i'm very new to Mathematica and this is my first problem. I define a
> function that is 0 everywhere:
> t[i_] := 0
> expect for point i =3 that is:
> t[3] = 1
> If now i evaluate the finite sum i obtain 1 as expected
> Sum[ t[i], {i, 1, 10}]
> Out = 1
> but if i try do the same with infinity i obtain
> In[808]:= Sum[ t[i], {i, 1, Infinity}]
> Out[808]= 0
> instead of 1 expected. Any advice?
>
> tb
>

What do you mean by "advice"? This is exactly the expected behaviour.  
When you evaluate Sum[ t[i], {i, 1, 10}] Mathematica simply adds up  
the 10 numbers, one of them being 3 and the other all 0, you get zero.  
When you evaluate Sum[ t[i], {i, 1, Infinity}] Mathematica does not  
try to add up infinitely many numbers because it can't be done 0. It  
never, ever sees the value t[3].
All this shows is that computer programs are not human, which is  
hardly surprising.

However, this works as you intended:

Sum[KroneckerDelta[i, 3], {i, 1, Infinity}]

1

Andrzej Kozlowski


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