Question

Trace Algorithm 1 when it is given n = 5 as input. That is, show all steps used by Algorithm 1 to find 5!, as is done in Example 1 to find 4!.

Short answer

The value of 5 ! is 120 .

Step-by-step solution

Recursive definition

From the recursive definition, the formula is:

0 ! = 1

n ! = n (n - 1)!

Determine the value of  5!

Evaluate the recursive definition at n = 5 .

$\begin{array}{r}5!=5\cdot 4!\\ =5\cdot 4\cdot 3!\\ =20\cdot 3!\\ =20\cdot 3\cdot 2!\end{array}$

Simplify further.

$\begin{array}{r}5!=60\cdot 2!\\ =60\cdot 2\cdot 1!\\ =120\cdot 1!\\ =120\end{array}$

Therefore, the value of 5! is 120 .