Re: Limit a^n / n!

• To: mathgroup at smc.vnet.net
• Subject: [mg8291] Re: [mg8130] Limit a^n / n!
• From: weber at math.uni-bonn.de (Matthias Weber)
• Date: Sun, 24 Aug 1997 04:46:32 -0400
• Organization: RHRZ - University of Bonn (Germany)
• Sender: owner-wri-mathgroup at wolfram.com

```In article <5tbh7i\$jeo at smc.vnet.net>, seanross at worldnet.att.net wrote:

> agt801 wrote:
> >
> > Hi,
> >
> > Would anyone tell me how to teach mathematica to evaluate the limit :
> >
> > Limit[a ^ n  / n!, n -> Infinity]  where a is a real constant.
> >
> > Leung
>
> Why not graph it as a function of n?  If there is a limit, you will see
> it soon enough.  Don't get hung up on the abstract concept of infinity.
> There are no infinities in nature, only in the human mind when used as a
> useful mathematical abstraction. In the real world, Infinity just means
> larger than you can measure or so large that it becomes the dominant
> signal in your measurement.  I just did this for a few values of a and
> it sure looks like the limit is zero.  At least, 10^100/100! is around
> 10^-175, which is closed enough to zero for me when compared to the
> value of a or n.

Oh boy. Would you also graph
1.000001 ^ n / n^3 ?

Good luck!

Matthias

```

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