Expand Factorials: (n-2)! & (n-n')!

In summary, Expand Factorials refer to the process of simplifying or expanding factorial expressions, specifically (n-2)! and (n-n')!. This involves using factorials, which are mathematical functions denoted by an exclamation mark and used to calculate the product of a given number and all positive integers less than it. The expressions can be expanded using specific formulas and can be further simplified using algebraic manipulation. The purpose of expanding factorials is to simplify complex expressions and it has various applications in fields such as probability and statistics. There are special cases to consider when expanding these expressions, such as when n is equal to 2 or n'.
  • #1
khary23
93
6
I know how to expand a factorial of the form (n-2)!. How would one expand (n-n')! ?
Would it just be (n-n')?
thanks in advance
 
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  • #2
What do you mean expand ? The factorial is just a <shortening> of a product, so by my records <expanding> it means expressing the whole terms explicitely (if many, maybe use the <...> sign).
 
  • #3
What I meant is how does one write (n-n')! For example n!= n(n-1)(n-2)...
 
  • #4
n!=(n)(n-1)(n-2)...(2)(1)

Therefore, (n-n')! is just n-n' substituted for all n above, thus

(n-n')(n-n'-1)(n-n'-2)...(2)(1).
 
  • #5
Ok thought it was that simple. thank you!
 

What are "Expand Factorials: (n-2)! & (n-n')!"?

Expand Factorials refer to the process of simplifying or expanding a factorial expression. In this case, we are looking at two specific expressions: (n-2)! and (n-n')!. These expressions involve the use of factorials, which are mathematical functions denoted by an exclamation mark (!) and used to calculate the product of a given number and all the positive integers less than it.

How do you expand (n-2)! and (n-n')!?

To expand (n-2)!, we can use the formula n! = n(n-1)(n-2)...3*2*1. Similarly, to expand (n-n')!, we can use the formula n! = n(n-1)(n-2)...(n-n'+1)(n-n').

What is the purpose of expanding factorials?

Expanding factorials can help simplify complex mathematical expressions and make them easier to solve or understand. It is also used in various fields of science, such as probability and statistics, to calculate the number of possible outcomes or combinations.

Can (n-2)! and (n-n')! be simplified further?

Yes, (n-2)! and (n-n')! can be further simplified using algebraic manipulation. For example, we can factor out common terms or use properties of factorials, such as n! = n*(n-1)! to simplify the expressions.

Are there any special cases for expanding (n-2)! and (n-n')!?

Yes, there are some special cases to consider when expanding (n-2)! and (n-n')!. For example, when n = 2, (n-2)! becomes 0! which is equal to 1. When n = n', (n-n')! becomes 0! which is also equal to 1.

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