Imum Coeli
Junior Member
- Joined
- Dec 3, 2012
- Messages
- 86
Hi I was wondering if anyone could help me solve this sum by hand.
\(\displaystyle \sum_{k=0}^{N} \frac{(N-k+L_0-x_0)!(x_0+k-1)!}{(k-1)!(N-k)!} \)
I've expanded it out but that is as far as I can get. I know (from wolfram) that the answer should be
\(\displaystyle \frac{x_0!(N+L_0-1)!(L_0-x_0-1)!}{L_0!(N-1)!} \)
Any help would be much appreciated. Thanks.
\(\displaystyle \sum_{k=0}^{N} \frac{(N-k+L_0-x_0)!(x_0+k-1)!}{(k-1)!(N-k)!} \)
I've expanded it out but that is as far as I can get. I know (from wolfram) that the answer should be
\(\displaystyle \frac{x_0!(N+L_0-1)!(L_0-x_0-1)!}{L_0!(N-1)!} \)
Any help would be much appreciated. Thanks.