Fun with zero sums
- To: mathgroup at smc.vnet.net
- Subject: [mg77133] Fun with zero sums
- From: "David W.Cantrell" <DWCantrell at sigmaxi.net>
- Date: Mon, 4 Jun 2007 03:56:56 -0400 (EDT)
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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