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Re: Fun with zero sums


On Mon, 4 Jun 2007, David W.Cantrell wrote:

> I'm using Mathematica 5.2; if Mathematica 6 behaves differently, I'd be
> interested to know it.
>
> In[1]:= Sum[0, {n, 1, Infinity}]
>
> Out[1]= 0
>
> which is as, I think, it should be. But then we have the following sums,
> which all disappoint, in different ways.
>
> In[2]:= Sum[0^n, {n, 1, Infinity}]
>
> Out[2]= Sum[0^n, {n, 1, Infinity}]
>
> In[3]:= Sum[0^(2*n - 1), {n, 1, Infinity}]
>
> Warning about "Infinite expression encountered."
>
> Out[3]= ComplexInfinity
>
> In[4]:= Sum[0^(2*n + 1), {n, 1, Infinity}]
>
> Warning about "Indeterminate expression encountered."
>
> Out[4]= Indeterminate
>
> Of course, Out[2..4] should have been 0, just like Out[1].
>
> David W. Cantrell
>
Hello David,

Thank you for these examples showing problems with sums involving 
powers of 0.

The incorrect answers in Out[3] and Out[4] are due to a missing check
for 0 while trying to simplify the summand in each case. As noted by
others, In[2] returns 0 in Mathematica 6. We will continue to work
on improved handling of important special cases such as the ones
given by you.

I apologize for the inconvenience caused by the incorrect behavior.

Sincerely,

Devendra Kapadia,
Wolfram Research, Inc.


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