Question

Trace Algorithm 1 when it is given n = 6 as input. That is, show all steps used by Algorithm 1 to find 6!, as is done in Example 1 to find 4!.

Short answer

The value of 6 ! is 720 .

Step-by-step solution

Recursive definition

From the recursive definition, the formula is as follows:

0! = 1

n! = n (n-1)!

Determine the value of  6!

Evaluate the recursive definition at n = 6 .

$\begin{array}{r}6!=6\cdot 5!\\ =6\cdot 5\cdot 4!\\ =30\cdot 4!\\ =30\cdot 4\cdot 3!\end{array}$

Simplify further.

$\begin{array}{r}6!=120\cdot 3!\\ =120\cdot 3\cdot 2!\\ =360\cdot 2!\\ =360\cdot 2\cdot 1!\end{array}$

Simplify further.

$\begin{array}{r}6!=720\cdot 1!\\ =720\cdot 1\cdot 0!\\ =720\cdot 1\\ =720\end{array}$

Therefore, the value of 6! is 720.