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Proving this Limit

  1. Sep 29, 2004 #1
    I'm a little stuck in my proof here. As I was trying to prove that the limit of a binomial distribution is the poisson distribution, I encountered this:

    [tex]

    \lim_{n\to +\infty} \frac{n!}{(n-x)! (n-k)^x}

    [/tex]

    where x and k are arbitrary constants.


    The books say that this approaches 1, but shows no formal proof. How are we sure that this approaches 1 as n gets larger? In short, what's the formal proof?

    Thanx for any help
     
  2. jcsd
  3. Sep 29, 2004 #2

    Hurkyl

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    Let's see... you have n things multiplied together on the top (1, 2, 3, ..., n), and you have n things multipled together on the bottom: (n - x) of them in (n-x)! and x of them in (n-k)^x. My first instinct would be to try and group terms in the numerator with terms in the denominator.
     
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