- #1
straycat
- 184
- 0
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
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