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Is there an identity $\sum_{r=0}^{l-1-p} \binom {r}{p} = \binom{l}{p+1}$ ? I need a proof for this, if it holds. For $l=2$ I can see that it is true.

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up vote 1 down vote accepted

I'd rather state: $$ \sum_{r=p}^{m}\binom{r}{p}=\binom{m+1}{p+1},$$ that can be proven by induction on $m$, since: $$\binom{m+1}{p+1}=\binom{m}{p}+\binom{m}{p+1}.$$

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Is this an equivalent formula ? –  AlexisZorbas Nov 19 '12 at 10:51
    
Ok, i think my formula is wrong, it has to be $\sum_{r=p}^{l-1}$. –  AlexisZorbas Nov 19 '12 at 11:03

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