- #1
Pietjuh
- 76
- 0
Hello everyone!
I'm trying to prove the following identity, but I'm not very lucky in finding the proof:
[tex]
{{n+k-1}\choose{n-1}} = \sum_{i=1}^k {k-1\choose i-1}{n\choose i}\,\, 1\leq k \leq n
[/tex]
I've tried to interpret this as a combinatorial problem, and I know the left hand side is the number of k-repeatingcombinations (don't really know the english word for it. The dutch word is k-herhalingscombinaties). But how i can transfer this to the sum on the right hand side...
Can someone help me a bit with this?
I'm trying to prove the following identity, but I'm not very lucky in finding the proof:
[tex]
{{n+k-1}\choose{n-1}} = \sum_{i=1}^k {k-1\choose i-1}{n\choose i}\,\, 1\leq k \leq n
[/tex]
I've tried to interpret this as a combinatorial problem, and I know the left hand side is the number of k-repeatingcombinations (don't really know the english word for it. The dutch word is k-herhalingscombinaties). But how i can transfer this to the sum on the right hand side...
Can someone help me a bit with this?