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Re: Limit a^n / n!

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

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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