Proof

(related to Proposition: Alternating Sum of Binomial Coefficients)

The closed formula for the alternating sum of binomial coefficients. \[\sum_{k=0}^n (-1)^n\binom nk=0\] follows immediately from the binomial theorem. \[\sum_{k=0}^n{n\choose k}x^{n-k}y^k=(x+y)^n\] by setting \(x=1\) and \(y=-1\).


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References

Bibliography

  1. Forster Otto: "Analysis 1, Differential- und Integralrechnung einer Veränderlichen", Vieweg Studium, 1983