What would be a combinatorial approach to find out $\sum\limits_{r=0}^{n}\binom{n+r}{r}$?
2026-03-31 21:56:33.1774994193
What is the result of $\sum\limits_{0}^{n}\binom{n+r}{r}$
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We have $\sum\limits_{r=0}^n\binom{n+r}{r}=\sum\limits_{r=0}^n\binom{n+r}{n}$. The second sum is equal to $\binom{2n+1}{n+1}$ by the more general hockey stick identity.