I'm having a difficult time understanding how to give a combinatorics proof of the identity $$\sum_{k=0}^{n} \binom{x+k}{k}=\binom{x+n+1}{n}$$
How can i prove the identity $\sum_{k=0}^{n} \binom{x+k}{k}=\binom{x+n+1}{n}$
$\begingroup$
combinatorics
summation
binomial-coefficients