Problem with limits involving a summation

  • Thread starter straycat
  • Start date
Hello all,

I am trying to prove that the following is true:

[tex]
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
[/tex]

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?

David
 

Hurkyl

Staff Emeritus
Science Advisor
Gold Member
14,847
17
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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