PDA

View Full Version : Problem with limits involving a summation


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

Hurkyl
Jul10-05, 09:15 AM
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.