Chapter 11.4, Problem 6E

To determine

To Prove: $\frac{n^2-3n}{2}$ is true for $n=3$ .

Answer to Problem 6E

It is prove that, by the Principle of Mathematical Induction $P\left(n\right)$ is false for $n=3$ .

Explanation of Solution

Given information: $\frac{n^2-3n}{2}$

Let the statement $P\left(n\right)$ given as

  $P\left(n\right)$ : $\frac{n^2-3n}{2}$ is true for $n=3$ .

We observe that $P\left(3\right)$ is true,

Since,

  $\begin{array}{l}=\frac{3^2-3\times 3}{2}\\ =\frac{9-9}{2}\\ =0\end{array}$

Therefore, $P\left(n\right)$ : $\frac{n^2-3n}{2}$ is false for $n=3$ , since a polygon must have at least three sides.