Integers from 1 to N are randomly generated . Each integer has an equal probability of being selected and unlimited repetition is permitted. A running sum is maintained.
Given any integer k, such that 1 <= k <= n , what is the probability that a sum of EXACTLY n will be reached?
Probabilities of Partial Sums
Let P(n,k) be the probability that a run using the integer n will produce a sum of exactly k.