Binomial Theorem · Exercise 51

Find $\left(\begin{array}{c}n\\ k-1\end{array}\right)+\left(\begin{array}{c}n\\ k\end{array}\right)$ and write the answer as a binomial coefficient in the form $\left(\begin{array}{c}n\\ k\end{array}\right).$ Prove it. Hint: Use the fact that, for any integer $p,$ such that $p\ge 1,p!=p\left(p-1\right)!.$

Its source prints no answer for this problem, so there's nothing to check against.

OpenStax, Algebra and Trigonometry 2e · §13.6 Binomial Theorem · Exercise 51