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Re: Fun with zero sums


$Version

6.0 for Mac OS X x86 (32-bit) (April 20, 2007)

Sum[0, {n, 1, Infinity}]

0

Sum[0^n, {n, 1, Infinity}]

0

Sum[0^(2*n - 1), {n, 1, Infinity}]

ComplexInfinity

Sum[Simplify[0^(2*n - 1), n >= 1], {n, 1, Infinity}]

0

Sum[0^(2*n + 1), {n, 1, Infinity}]

Indeterminate

Sum[Simplify[0^(2*n + 1), n >= 0], {n, 0, Infinity}]

0


Bob Hanlon

---- "David W.Cantrell" <DWCantrell at sigmaxi.net> 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
> 



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