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