You need to realize that:askor said:How do you get
(n + 1)! = (n + 1)(n)(n - 1)(n - 2) ... 3 ⋅ 2 ⋅ 1
?
Isn't (n + 1)! = (n + 1) ⋅ (n + 1 - 1) ⋅ (n + 1 - 2) ⋅ (n + 1 - 3) ⋅ (n + 1 - 4) ... and so on?
The formula for factorial (n+1) is (n+1)! = (n+1) x n x (n-1) x ... x 3 x 2 x 1. This means multiplying all the numbers from (n+1) down to 1.
To calculate factorial (n+1), you can use a calculator or do it manually by multiplying all the numbers from (n+1) down to 1. For example, if n=5, then (n+1)! = 6 x 5 x 4 x 3 x 2 x 1 = 720.
The difference between factorial n and factorial (n+1) is that factorial (n+1) includes an extra factor of (n+1), whereas factorial n does not. For example, if n=4, then factorial n = 4 x 3 x 2 x 1 = 24, and factorial (n+1) = 5 x 4 x 3 x 2 x 1 = 120.
Factorial (n+1) is commonly used in mathematics to represent the number of ways to arrange a set of n+1 objects. It is also used in probability and combinatorics to calculate permutations and combinations.
No, factorial (n+1) cannot be negative. Factorial is defined only for non-negative integers, as it represents a counting process. Therefore, it is not meaningful to calculate a factorial for negative numbers.