I like the following binomial identity in that the RHS extracts the indeterminate $w$ from the LHS.



> 
> **Question.** Can you show that
>  $$\sum\_{k=0}^n\binom{x+kw}k\binom{y-kw}{n-k}=\sum\_{k=0}^n\binom{x+y-k}{n-k}w^k\,\,\,?$$
> 
> 
> 


It would be great if we can see alternative proofs? I've a bias for combinatorial arguments. :-)



An interesting identity: in search of a proof -Part I
This is known as Jensen's identity and dates back to 1902. See here an overview of this identity and related ones, and a proof: <https://arxiv.org/abs/1005.2745>, a paper by Victor Guo.


