1. FACTORIALS
Dr. Shildneck

2. What Does Factorial Mean?
N! (stated “n factorial”) is defined as the product of every consecutive positive integer, in decreasing order, from N to 1.
For example,
5! = 5 x 4 x 3 x 2 x 1 = 120

3. n! = (1)(2)(3)(4)…(n-2)(n-1)(n).
Formal Definition
If n is a positive integer, n factorial is defined as
n! = (1)(2)(3)(4)…(n-2)(n-1)(n).
*A special case of n! is 0! Which is defined to be equal to 1.
0! = 1

4. Order of Operations Factorials follow the order of operations.
For example:
1. 2n!
2. (2n)!

5. Examples
1. Find the first five terms of the sequence defined by

6. Examples
2. Write the explicit rule for the following sequence.
6, 24, 120, 720, 5040, …

7. Examples
3. Evaluate.

8. Examples
4. Evaluate.

9. Examples
5. Simplify.

10. Examples
6. Simplify.

11. Assignment
Worksheet – Assignment #2