Factorial Notation

Let Us Learn About Factorial Notation.


Question:What is Factorial Notation?
Answer: Let n be a positive integer. The continued product of first n natural numbers is called factorial n and is denoted as n

The notation n! represents the product of first n natural
numbers, i.e., the product 1 × 2 × 3 × . . . × (n – 1) × n is denoted as n!. We read this
symbol as ‘n factorial’. Thus, 1 × 2 × 3 × 4 . . . × (n – 1) × n = n !
1 = 1 !
1 × 2 = 2 !
1× 2 × 3 = 3 !
1 × 2 × 3 × 4 = 4 ! and so on.

We define 0 ! = 1
We can write 5 ! = 5 × 4 ! = 5 × 4 × 3 ! = 5 × 4 × 3 × 2 !
= 5 × 4 × 3 × 2 × 1!

Clearly, for a natural number n
n ! = n (n – 1) !
= n (n – 1) (n – 2) ! [provided (n ≥ 2)]
= n (n – 1) (n – 2) (n – 3) ! [provided (n ≥ 3)]
and so on.