Cyclic identity with binomials

#cyclic#binomial#identity

Statement

Show that $\binom{n}{k}+\binom{n}{k+1}=\binom{n+1}{k+1}$ .

Hint

Pascal's identity with indices shifted.

Show solutionHide solution

Pascal. $\binom{n+1}{k+1}=\binom{n}{k}+\binom{n}{k+1}$ .

Conclusion. The identity holds.