Factorials and anti-factorials Supposing n¡ (the inverted spanish exclamation mark - as opposed to n!) uses sequential divisions, is it always true that n! * n¡ = n^2 ? Example: For n = 7, n¡=7-:6-:5-:4-:3-:2 = 0.00972222222222222222222222222222. If you multiply this number by 5040 (=7!) you get 49.

Kailey Vargas 2022-09-13 Answered
Factorials and anti-factorials
Supposing n¡ (the inverted spanish exclamation mark - as opposed to n!) uses sequential divisions, is it always true that n ! n ¡ = n 2 ? Example: For n = 7,
n ¡ = 7 ÷ 6 ÷ 5 ÷ 4 ÷ 3 ÷ 2 = 0.00972222222222222222222222222222. If you multiply this number by 5040 (=7!) you get 49.
I've read the directions in the help center and could not understand why it is off topic. It is like asking about the relation between x x = x 2 and x ÷ x ÷ x ÷ x = x 2 . In fact, I could not determine if this kind of question is on-topic either. And I think there is not a sister-site that would accept such kind of questions (I checked all of them). Anyways, my question has been answered. I was lazy when I failed to do some calculations to find the answer myself. This was my very first time here. I've learned something. Thank you.
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Answers (2)

empatiji2v
Answered 2022-09-14 Author has 18 answers
By your definition it's
n ( n 1 ) ! n ! = n 2

We have step-by-step solutions for your answer!

Leroy Gray
Answered 2022-09-15 Author has 3 answers
Your definition amounts to
n ¡ = n ( n 1 ) !
so for instance, we would compute 7 ¡ = 7 / ( 6 ! ). Clearly, then, we have
( n ! ) ( n ¡ ) = [ n ( n 1 ) ! ] n ( n 1 ) ! = n 2

We have step-by-step solutions for your answer!

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