Proposition: Sum of Binomial Coefficients III
For any element of a ring \(x\in(R,+,\cdot) \) and any natural number \(n\ge 0\) the following sum formula holds:
\[\sum_{k=0}^nk^2\binom nk(1-x)^{n-k}x^k=nx(1-x)+n^2x^2.\]
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References
Bibliography
- Bosch, Karl: "Elementare Einführung in die Wahrscheinlichkeitsrechnung", vieweg Studium, 1995, 6th Edition
