Contents
Factorial of a natural number n is written as n! and is considered as the product of all natural numbers from 1 to n (inclusive).
For n > 0:
n! = 1 ⋅ 2 ⋅ 3 ⋅ 4 … ⋅ n
For n = 0:
0! = 1
Content
Factorial Formula
examples:
- 1! = 1
- 2! = 1 ⋅ 2 = 2
- 3! = 1 ⋅ 2 ⋅ 3 = 6
- four! = 4 ⋅ 1 ⋅ 2 ⋅ 3 = 4
- 5! = 1 ⋅ 2 ⋅ 3 ⋅ 4 ⋅ 5 = 120
Recurrent factorial formula
examples:
- 5! = 5 ⋅ (5 – 1)! =
5 ⋅ 4! =5⋅24 = 120 - 7! = 7⋅ (7 – 1)! =
7 ⋅ 6! =5⋅720 = 5040
Stirling’s formula
Used to approximate factorial.
Example:
Factorial table
| 0 | 1 | |||||||||
| 1 | 1 | |||||||||
| 2 | 2 | |||||||||
| 3 | 6 | |||||||||
| 4 | 24 | |||||||||
| 5 | 120 | |||||||||
| 6 | 720 | |||||||||
| 7 | 5040 | |||||||||
| 8 | 40320 | |||||||||
| 9 | 362880 | |||||||||
| 10 | 3628800 | |||||||||
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