Question

True or False$n!=\frac{(n+1)!}{n}$.

Short answer

The given statement is false.

Step-by-step solution

Step 1. Given infomation.

The given statement is:

$n!=\frac{(n+1)!}{n}$

Step 2. Determine whether the given statement is true or false.

The right-hand side of the equation can be written as:

$\begin{array}{rcl}\frac{(n+1)!}{n}& =& \frac{(n+1)·n!}{n}\\ \frac{(n+1)!}{n}& =& \frac{(n+1)}{n}·n!\\ \frac{(n+1)!}{n}& \ne & n!\end{array}$

Step 3. Conclusion.

The given statement is false.