1. binomial coefficient proof

I'm asked to show that ${n \choose k} = \sum^{k+1}_{i=1}{n-i \choose k-i+1}$ for all positive integers 0 <= k <= n.

I've tried using pascal's identity in combination with mathematical induction, but I can't seem to prove this. Please help.

2. Have you tried expanding out the first few and last few terms of the summation on the RHS?

3. i see now. one can prove this by applying pascals identity several times