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MathGroup Archive 2007

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Re: Fun with zero sums

  • To: mathgroup at smc.vnet.net
  • Subject: [mg77175] Re: Fun with zero sums
  • From: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
  • Date: Tue, 5 Jun 2007 06:42:34 -0400 (EDT)
  • Organization: The Open University, Milton Keynes, UK
  • References: <f40hfg$6km$1@smc.vnet.net>

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

Hi David,

Here is the results from version 6.

In[1]:= Sum[0, {n, 1, Infinity}]

Out[1]= 0

In[2]:= Sum[0^n, {n, 1, Infinity}]

Out[2]= 0

In[3]:= Sum[0^(2*n - 1), {n, 1, Infinity}]

During evaluation of In[3]:= Power::infy:Infinite expression 1/0 \
encountered. >>

Out[3]= ComplexInfinity

In[4]:= Sum[0^(2*n + 1), {n, 1, Infinity}]

During evaluation of In[4]:= \[Infinity]::indet:Indeterminate \
expression 0 SymbolicSum`var$202^2 $Failed^2 \[Infinity] encountered. \
 >>

Out[4]= Indeterminate

Cheers,
Jean-Marc


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