The following binomial coefficient property, $\displaystyle \sum_{s=0}^{n-1}\binom{k+s}{k}=\binom{n+k}{k+1}$, is described in the book Mathematical Methods for Physics and Engineering—by K.F.Riley—with n being the number of terms, the s being the lower summation index, and k being a fixed parameter. However, I do not understand how the three variables work in this formula as I am only used to seeing two variables (K and N usually) in the binomial coefficient properties. Please, if you could, describe what this formula means and the role each of the three variables play in the formula.
2026-04-06 22:10:47.1775513447
What does this binomial coefficient property mean?
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