binomial coefficient and recurrence relation

Asked Dec 02 '14 at 14:54

Active Dec 02 '14 at 15:18

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any hints on how to solve the recurrence relations for the following binomial coefficient

\begin{equation} {n \choose k}=\begin{cases} 1, & \text{if $k\in\{0,n\}$}.\\ {n-1 \choose k-1}+{n-1 \choose k}, & \text{otherwise}. \end{cases} \end{equation} for $ 0\ge k \le n $

edited Dec 02 '14 at 15:18

asked Dec 02 '14 at 14:54

fudu

Sometimes known as the Pascal Identity. Several combinatorial proofs have been given on MSE, also "algebraic" proofs. Wikipedia, now that you know the name,might also help. – André Nicolas Dec 02 '14 at 15:04
What's the question? This is a recurrence relation. – Jean-Claude Arbaut Dec 02 '14 at 15:14
I don't see the relation to the post you have mentioned @peterwhy – fudu Dec 02 '14 at 15:24
Sorry, I now noticed you reverted another editor's change, back to $0\ge k \le n$. Do you wish to ask about the case where $k\le 0$? – peterwhy Dec 02 '14 at 15:26
Nope that's the part where i need hint @peterwhy – fudu Dec 02 '14 at 15:28

binomial coefficient and recurrence relation

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