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 \(n\in\mathbb N\).

| | | | | created: 2014-10-12 10:36:02 | modified: 2020-06-16 19:25:43 | by: bookofproofs | references: [977]

1.Proof: (related to "Recursive Formula for Binomial Coefficients") 

2.Proof: (related to "Recursive Formula for Binomial Coefficients")