Derivative of the binomial upper tail

Derivative of the binomial upper tail in the success probability: for 1 ≤ k ≤ n, d/dp P(Bin(n, p) ≥ k) = n C(n - 1, k - 1) p^(k-1) (1-p)^(n-k) at every real p (the sum telescopes).

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