For positive integers n, r show that:
C(n+r+1,r) = C(n+r,r) + C(n+r-1,r-1) + ... + C(n+2,2) + C(n+1,1) + C(n,0)
= C(n+r,n) + C(n+r-1,n) + ... + C(n+2,n) + C(n+1,n) + C(n,n)
Now, I've tried expanding the combinations, and I was able to get (n!) in the denominator of every term, though I'm not sure if that is even relevant to the proof. Not far, I know, but essentially, I'm stuck there and I don't know where to go.
Thanks in advance for any and all help.
Wow. Ha, we haven't even started with Induction yet, but in any case, thank you very much.
I'll study your response until I totally understand it!