[Date Index]
[Thread Index]
[Author Index]
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
>
Prev by Date:
**Hold and Simplify**
Next by Date:
**early version notebook in Mathematica 6 Linux**
Previous by thread:
**Re: Fun with zero sums**
Next by thread:
**Re: Fun with zero sums**
| |