Hey, first time poster here, this is the proof:

For positive integers j and k, 1<=j<=k, show that C(k+1,j) = C(k,j) +C(k,j-1)

I am at the point where I have numerator: [ k!(k-j-1)!(j-1)! + k!j!(k-j)! ]

over [ j!(j-1)!(k-j-1)!(k-j)! ]

Which i need to simplify.

Which is supposed to equal (k+1)! / (j!(k+1-j)!) I believe

I'm probably making this more confusing than it needs to be.

Thanks in advance.