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Problem with limits involving a summation

  1. Jul 9, 2005 #1
    Hello all,

    I am trying to prove that the following is true:

    lim_{M \rightarrow \infty} \sum_{P = (\frac{1}{N}-\delta)M}^{(\frac{1}{N}+\delta)M}
    \frac{(N-1)^{{M-P}}M!}{P!(M-P)!N^{M}} \rightarrow 1

    where [tex] P [/tex], [tex] M [/tex], and [tex] N [/tex] are integers, and [tex] \delta [/tex] is an arbitrarily small positive number (less than [tex] 1/N [/tex]).

    Any ideas on how I might approach this?

  2. jcsd
  3. Jul 10, 2005 #2


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    Staff Emeritus
    Science Advisor
    Gold Member

    Well, since you're doing statistics, can you interpret that summation as a probability? Maybe you know some things about the probability distribution that might help.
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