       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)

```\$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:= Sum[0, {n, 1, Infinity}]
>
> Out= 0
>
> which is as, I think, it should be. But then we have the following sums,
> which all disappoint, in different ways.
>
> In:= Sum[0^n, {n, 1, Infinity}]
>
> Out= Sum[0^n, {n, 1, Infinity}]
>
> In:= Sum[0^(2*n - 1), {n, 1, Infinity}]
>
> Warning about "Infinite expression encountered."
>
> Out= ComplexInfinity
>
> In:= Sum[0^(2*n + 1), {n, 1, Infinity}]
>
> Warning about "Indeterminate expression encountered."
>
> Out= Indeterminate
>
> Of course, Out[2..4] should have been 0, just like Out.
>
> David W. Cantrell
>

```

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