Can this equation $$ \sum_{k=m}^{n}\binom{k}{m}$$ be generalized to an expression?
$ \binom{n+1}{m+1}$ might be the solution
For example, if n=9, m=3
$ \binom{3}{3}+\binom{4}{3}+\binom{5}{3}+\binom{6}{3}+\binom{7}{3}+\binom{8}{3}+\binom{9}{3} = 210 = \binom{10}{4}$
But I'm not sure why and how to get to this equation.
