Chapter 11 - Sequences; Induction; the Binomial Theorem - Section 11.5 The Binomial Theorem - 11.5 Assess Your Understanding - Page 857: 45

Proved below.

We know that $\displaystyle{n\choose k}=\dfrac{n!}{(n-k)! \ k!}$. Therefore, $\displaystyle{n\choose{n-1}}=\dfrac{n!}{(n-1)!(n-(n-1))!}=\dfrac{n}{1!}=n$ and $\displaystyle{n\choose{n}}=\dfrac{n!}{(n)!(n-(n))!} =\dfrac{n!}{0!(n)!}=\dfrac{1}{1!}=1$ Thus, the result has been proved.