       Re: Limit a^n / n!

• To: mathgroup at smc.vnet.net
• Subject: [mg8245] Re: [mg8130] Limit a^n / n!
• From: seanross at worldnet.att.net
• Date: Thu, 21 Aug 1997 21:17:02 -0400
• Sender: owner-wri-mathgroup at wolfram.com

```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.

```

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