Re: Fun with zero sums

*To*: mathgroup at smc.vnet.net*Subject*: [mg77390] Re: [mg77133] Fun with zero sums*From*: Devendra Kapadia <dkapadia at wolfram.com>*Date*: Thu, 7 Jun 2007 04:08:46 -0400 (EDT)*References*: <200706040756.DAA06337@smc.vnet.net>

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.

**References**:**Fun with zero sums***From:*"David W.Cantrell" <DWCantrell@sigmaxi.net>