(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Prove that the following binomial identity holds:

[tex]{n+k-1 \choose k} = \sum_{i=1}^k {k-1\choose i-1}{n\choose i}[/tex]

3. The attempt at a solution

One of the methods i've tried is to use induction on the variable n, but while trying this I got stuk on rewriting the binomial coefficients.... can someone give me a hint if I can use another simple binomial identity for this?

Another thing I have tried to do is to look at the generating function of the left hand side, and then try to rewrite this to a generating function for the right hand side, but that didn't succeed either....

Can someone point me a little bit in the right direction?

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# Homework Help: Binomial identity

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