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Difference between revisions of "Factorial number"
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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 ≥ 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 | ||
− | + | ==See also== | |
+ | *[[Multifactorial number]] | ||
==External links== | ==External links== | ||
− | *[ | + | *[[Wikipedia:Factorial|Factorial]] |
− | [[Category: | + | [[Category:Number]] |
Revision as of 12:47, 25 March 2019
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 ≥ 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