Howdy folks, I have an interesting math problem that eludes 6 math geeks and 2 college professors, although we can't assume that the profs are working on this problem.
Now
s does exist... and supposedly it is 1/2. I wont discuss any of my work---other than it is wrong. I understand why it is wrong, finally. I would love some ideas to be spit-balled.
SOLUTION:
I finally solved this beast to my satisfaction. First, one needs to see that the limit has ties to the Poisson Distribution. One can prove that the asymmetric Poisson Distribution becomes symmetric as the expectant value, lambda or here denoted as n, goes to infinity. This means that the probability above n and below n are equal to one another. Next, one can use Stirling's Approximation to show that the probability of n occurrences occurring as n goes to infinity is also zero. Finally, it is simple algebra to show that the sum of P"below n", P"of n", and P"above n" equals 1, where P"below n" is equal to P"above n" and P"of n" is zero, then 2 * P"below n" = 1, and P"below n" is 1/2. Therefor, the limit is equal to P"below n" plus P"of n", and is equal to 1/2.