Give combinatorial or bijective proofs of the following. Part of your job is to determine all values of n,k, and/or m for which the identities are valid.
I can't get very far with this one either. I notice that all terms on the left hand side are zero until we get to . Then I calculate all terms equal 1, so we have n-m terms which makes the left hand side equal n-m.
The right hand side I get
I can get no further.
Can someone help or tell me if I have the whole combinatorial proof thing wrong.