Running Sum of Randomly Generated Numbers

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.

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