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- Factorial, but with addition - Mathematics Stack Exchange
Is there a notation for addition form of factorial? $$5! = 5\times4\times3\times2\times1$$ That's pretty obvious But I'm wondering what I'd need to use to describe $$5+4+3+2+1$$ like the factorial $5!$ way EDIT: I know about the formula I want to know if there's a short notation
- What does the factorial of a negative number signify?
For example: the factorial of zero i e an empty set ( doesn't occur) is 1 As the empty set can be arranged only in 1 way - i e by filling nothing Now, let's take an example: 5 distinct seats How many ways 5 distinct seats can be arranged? - 5! ways i e 120 So, basically, factorial gives us the arrangements
- factorial - Why does 0! = 1? - Mathematics Stack Exchange
$\begingroup$ The theorem that $\binom{n}{k} = \frac{n!}{k!(n-k)!}$ already assumes $0!$ is defined to be $1$ $ Otherwise this would be restricted to $0 <k
- Can the factorial function be written as a sum?
In this paper we give an additive representation of the factorial, which can be proven by a simple quick analytical argument We also present some generalizations, which are linked, on the one hand to an arithmetical theorem proven by Euler (decomposition of primes as the sum of two squares), and, on the other hand, to modern combinatorics
- Factorial number of digits - Mathematics Stack Exchange
This is a slightly more accurate approximation that Sterling's approximation, given that you wanted to take the factorial of a relatively small number like 20 We can express this alternatively as, $$\log_{10} n! \approx n \log_{10} n - 0 434 n + \log_{10} (2 \pi n)$$
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