Factorial Notation

Today we learned about factorial notation. The symbol n! (read as n factorial) means to multiply all of the positive integers from n all the way down to one (1).

FORMULA USED: n!= n(n-1)(n-2)...(3)(2)(1), where n is an element of the positive integers.

Example 4:

5!= ----->n=5 so when you plug in to the formula you get:

5(5-1)(5-2)(5-3)(5-4)

(5)(4)(3)(2)(1)

=120

We can remember these factorials:

• 0!= 1
• 1!= 1
• 2!= 2
• 3!= 6
• 4!= 24
• 5!= 120
• 6!= 720
• 7!= 5040
• 8!= 40320
• 9!= 362880
• 10!= 3628800

We can also simplify factorial equations:

Example 5:

a) 5!/4! ----->we can expand the 5! to (5)(4!)

(5)(4!)/4! ----->and the (4!)'s are able to cancel out each other leaving the (5)

=5

e) (s-2)!/(s+1)! ----->we can expand the (s+1)! into: (s+1)(s+0)(s-1)(s-2)!

(s-2)!/(s+1)(s+0)(s-1)(s-2)! -----> since there are two (s-2)!'s in both the numerator and the denominator, they can cancel out leaving us with the answer

=1/(s+1)(s+0)(s-1)