straycat
Jul9-05, 11:56 PM
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 P , M , and N are integers, and \delta is an arbitrarily small positive number (less than 1/N ).
Any ideas on how I might approach this?
David
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 P , M , and N are integers, and \delta is an arbitrarily small positive number (less than 1/N ).
Any ideas on how I might approach this?
David