1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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:


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


    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


    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    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.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook