Re: Fun with zero sums

*To*: mathgroup at smc.vnet.net*Subject*: [mg77155] Re: [mg77133] Fun with zero sums*From*: Bob Hanlon <hanlonr at cox.net>*Date*: Tue, 5 Jun 2007 06:32:13 -0400 (EDT)*Reply-to*: hanlonr at cox.net

$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 >