Chapter 9, Problem 101RE

To determine

To find whether the given statement or expression is true or false.

Answer to Problem 101RE

The statement is false as left-hand side is not equal to right hand side.

Explanation of Solution

Given:

The equation:

  $\frac{\left(n+2\right)!}{n!}=\frac{\left(n+2\right)}{n}$

To find if

  $\frac{\left(n+2\right)!}{n!}=\frac{\left(n+2\right)}{n}$

Can be written as

  $\begin{array}{l}\frac{\left(n+2\right)!}{n!}=\frac{\left(n+2\right)\left(n+1\right)n!}{n!}\\ =\left(n+2\right)\left(n+1\right)\end{array}$

Hence, the given statement is false.