Chapter 1.13, Problem 3P

Show that if p is a positive integer, then $\left(\begin{array}{l}p\\ n\end{array}\right)=0$ when n > p, so ${(1+x)}^p={\displaystyle \sum \left(\begin{array}{l}p\\ n\end{array}\right)}{x}^n$ is just a sum of p+1 terms, from n = 0 to n = p. For example, ${(1+x)}^2$ has 3 terms, ${(1+x)}^3$ has 4 terms, etc. This is just the familiar binomial theorem.