Chapter 9.9, Problem 18ES

If m is any real number, and $k$ is a nonnegative integer, then we define the binomial coefficient

$\begin{array}{l}\left(\begin{array}{c}m\\ k\end{array}\right)\text{by}\text{the}\text{formulas}\left(\begin{array}{c}m\\ 0\end{array}\right)=1\text{and}\\ \left(\begin{array}{c}m\\ k\end{array}\right)=\frac{m(m-1)(m-2)\cdot \cdot \cdot (m-k+1)}{k!}\end{array}$

For $k>1.$ Express Formula (17) in the text in terms of binomial coefficients.