Proposition: Sum of Binomial Coefficients I

For any element of a ring \(x\in(R,+,\cdot) \) and any natural number \(n\ge 0\) the following sum formula holds:

\[\sum_{k=0}^n\binom nk(1-x)^{n-k}x^k=1.\]

Proofs: 1

Proofs: 1 2


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References

Bibliography

  1. Bosch, Karl: "Elementare Einf├╝hrung in die Wahrscheinlichkeitsrechnung", vieweg Studium, 1995, 6th Edition