Lesson 2

Discover

 

You have seen that 10! = 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1.

 

If you let n = 10, then the preceding expression can be written as follows:

 

n! = n × (n − 1) × (n − 2) × (n − 3) × (n − 4) × (n − 5) × (n − 6) × (n − 7) × (n − 8) × (n − 9)

 

or

 

n! = n(n − 1)(n − 2)(n − 3 )…(3)(2)(1)

 

It is important to note that n! is only defined when n is a natural number.

 

Calculating the value of an expression involving factorial notation without a calculator can be a time-consuming process. In the following Try This, you will look for patterns that might exist between subsequent expressions involving factorial notation.

 

Try This 1

1. Complete a chart like the following. Read the hint provided in the second row if you need help.
   
   

   n!	n! in Expanded Form	Expression Involving n and (n − 1)!	Value of n!
   1!	1	1	1
   2!	2 × 1	2 × _!	2
   3!	3 × 2 × 1	3 × _!
   4!	_ × _ × _ × _	4 × _!
   5!	_ × _ × _ × _ × _	5 × _!
   6!	_ × _ × _ × _ × _ × _	6 × _!
   7!	_ × _ ×  _ × _ × _ × _ × _	7 × _!

2. Describe the relationship between n! and (n − 1)!.
3. Create a general expression relating n!, n, and (n − 1)!.

Save your responses in your course folder.