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Proposition: Recursive Formula for Binomial Coefficients

The binomial coefficient \(\binom nk\) can be for \(k,n\in\mathbb N\), \(n\ge 1\), \(n\ge k\) calculated using the following recursive formula:

\[\binom nk=\binom {n-1}{k-1} + \binom {n-1}{k}.\]

We have the special cases

\(\binom n0=1\) for all \(n\in\mathbb N\) and

\(\binom nn=1\) for all \(n\in\mathbb N\).

Table of Contents

Proofs: 1

Mentioned in:

Parts: 1 2
Proofs: 3 4 5

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References

Bibliography

1. Aigner, Martin: "Diskrete Mathematik", vieweg studium, 1993