Proof.

I was playing around with binomial expansion and came up with a nifty proof inspired by a question DFranklin helped me with.

$\binom {n} {r} \times \binom {n-r} {1} = (r+1) \times \binom {n} {r+1}$

Would this be useful anywhere?

This looks pretty cool, I'll try proving it tomorrow morning, when I wake up.
(did you prove it the way I have in my groggy head right now, i.e: factorial definition and then recombining into binomial coefficient?)

I can't immediately see where it's useful or comes handy, and I do suspect that if you ever come across such an occasion where it might be a shortcut, you won't remember this result anyway.

I was playing around with binomial expansion and came up with a nifty proof inspired by a question DFranklin helped me with.

$\binom {n} {r} \times \binom {n-r} {1} = (r+1) \times \binom {n} {r+1}$

Would this be useful anywhere?

I was playing around with binomial expansion and came up with a nifty proof inspired by a question DFranklin helped me with.

$\binom {n} {r} \times \binom {n-r} {1} = (r+1) \times \binom {n} {r+1}$

Would this be useful anywhere?

I was playing around with binomial expansion and came up with a nifty proof inspired by a question DFranklin helped me with.

$\binom {n} {r} \times \binom {n-r} {1} = (r+1) \times \binom {n} {r+1}$

Would this be useful anywhere?