Hello everyone!(adsbygoogle = window.adsbygoogle || []).push({});

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?

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Proving Combinatorial identity

**Physics Forums | Science Articles, Homework Help, Discussion**