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Difference between revisions of "Factorial number"
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(see also Factorial prime) |
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In [[mathematics]] symbolized by placing the "!" (known as the exclamation mark or bang) after a number, it represents multiplying a number by all [[whole number|whole numbers]] smaller than it. | In [[mathematics]] symbolized by placing the "!" (known as the exclamation mark or bang) after a number, it represents multiplying a number by all [[whole number|whole numbers]] smaller than it. | ||
| + | |||
| + | ==Definition== | ||
| + | A factorial is defined by the product | ||
| + | :<math>n! = 1 \cdot 2 \cdot 3 \cdots (n{-}2) \cdot (n{-}1) \cdot n</math> | ||
| + | for <math>n \ge 1</math>. | ||
| + | |||
| + | The same written as mathmatical product | ||
| + | :<math>n! = \prod_{i = 1}^n i.</math> | ||
| + | |||
| + | and as recurrence relation | ||
| + | :<math> n! = n \cdot (n-1)!</math> | ||
==Examples== | ==Examples== | ||
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:10! = 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 = 3628800 | :10! = 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 = 3628800 | ||
| − | Factorial | + | ==See also== |
| + | *[[Factorial prime]] | ||
| + | *[[Multifactorial number]] | ||
==External links== | ==External links== | ||
| − | *[ | + | *[[Wikipedia:Factorial|Factorial]] |
| − | [[Category: | + | [[Category:Number]] |
Latest revision as of 13:40, 5 November 2023
In mathematics symbolized by placing the "!" (known as the exclamation mark or bang) after a number, it represents multiplying a number by all whole numbers smaller than it.
Contents
Definition
A factorial is defined by the product
- [math]\displaystyle{ n! = 1 \cdot 2 \cdot 3 \cdots (n{-}2) \cdot (n{-}1) \cdot n }[/math]
for [math]\displaystyle{ n \ge 1 }[/math].
The same written as mathmatical product
- [math]\displaystyle{ n! = \prod_{i = 1}^n i. }[/math]
and as recurrence relation
- [math]\displaystyle{ n! = n \cdot (n-1)! }[/math]
Examples
- 5! = 5 * 4 * 3 * 2 * 1 = 120
- 10! = 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 = 3628800
