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Fun with zero sums


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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