$$\binom{r}{r}+\binom{r+1}{r}+\binom{r+2}{r}+...+\binom{n}{r}=\binom{n+1}{r+1}$$
I know how to prove this by induction.
But I got stuck with proving it combinatorially.
How do I start? and please give some directions.
how do I prove this formula combinatorially?
1
$\begingroup$
combinatorics
discrete-mathematics
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0Search the site for *hockey stick identity*. Most proofs probably use induction, but there may be combinatorial arguments also. – 2017-01-23
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0I actually came up with a combinatorial way of proving this. But that solution has already appeared [in this answer](http://math.stackexchange.com/a/1491698/11619), so I won't waste bandwidth by reposting it. – 2017-01-23
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0Actually scrolling further down the list of answers gives you [this](http://math.stackexchange.com/a/1490965/11619). The same idea but more verbose. – 2017-01-23