Loading [MathJax]/extensions/TeX/mathchoice.js

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.

Proofs: 1

Proofs: 1


Thank you to the contributors under CC BY-SA 4.0!

Github:
bookofproofs


References

Bibliography

  1. Bosch, Karl: "Elementare Einführung in die Wahrscheinlichkeitsrechnung", vieweg Studium, 1995, 6th Edition