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Chapter 3
 
FACTORIALS
 
A sequence which occurs frequently in mathematics is


We tabulate this in the form 

                                                  
                 n   0  1  2  3   4   5    6  ... 
                 n!  1  1  2  6  24  120  720 ...
 
where the notation n! (read as n factorial) is used for the number on the second line that is thus associated with n. Clearly 0! = 1, 1! = 1, 2! = 2, 3! = 6, 4! = 24, etc. The definition of n! can be given as follows:
 
0! = 1, 1! = 1(0!), 2! = 2(1!),
3! = 3(2!), ... , (n + 1)! = (n + 1)(n!), ... .
 
The expression n! is not defined for negative integers n. One reason is that the relation (n + 1)! = (n + 1)(n!) becomes  when n = -1, and hence there is no way to define (-1)! so that this relation is preserved.
 
 
Problems for Chapter 3
 
1. Find the following:

(a) 7!.

(b) (3!)2.

(c) (32)!.

(d) (3!)!.
 
2. Find the following:

(a) 8!.

(b) (2!)(3!).

(c)

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Monday, June 22, 1998