Answer
1! = 1 · 1 = 1, 2! = 2 · 1! = 2 · 1 = 2, 3! = 3 · 2! = 3 · 2 = 6,
4! = 4 · 3! = 4 · 6 = 24, and 5! = 5 · 4! = 5 · 24 = 120
Work Step by Step
--First,
we use the recursive step to write 5! = 5 · 4!.
-- We then use the recursive step
repeatedly to write
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, and 5! = 5 · 4! = 5 · 24 = 120.
