Answer
$1! = 1 . 1 = 1$,
$2! = 2 . 1! = 2 · 1 = 2$,
$3! = 3 . 2! = 3 · 2 = 6$,
$4! = 4 . 3! = 4 · 6 = 24$,
$5! = 5 . 4! = 5 · 24 = 120$
and $6! = 6 . 5! = 6 . 120 = 720$
Work Step by Step
First, we use the recursive step to write $6! = 6 . 5!$
We then use the recursive step repeatedly to write
$5!= 5 . 4!$;
$4! = 4 . 3!$;
$3! = 3 . 2!$;
$2! = 2 . 1!$;
and $1! = 1 . 0!$
Inserting the value of $0! = 1$, and working back through the steps, we see that
$1! = 1 . 1 = 1$,
$2! = 2 . 1! = 2 · 1 = 2$,
$3! = 3 . 2! = 3 · 2 = 6$,
$4! = 4 . 3! = 4 · 6 = 24$,
$5! = 5 . 4! = 5 · 24 = 120$
and $6! = 6 . 5! = 6 . 120 = 720$
