Sum of Binomial Coefficients over Upper Index

Theorem
Let $$m \in \Z$$ be an integer such that $$m \ge 0$$.

Then:
 * $$\sum_{j=0}^n \binom j m = \binom {n+1} {m+1}$$

where $$\binom j m$$ denotes a binomial coefficient.

That is:
 * $$\binom 0 m + \binom 1 m + \binom 2 m + \cdots + \binom n m = \binom {n+1} {m+1}$$

Proof
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