What is the Notation for Factorials?

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    Factorials Notation
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Discussion Overview

The discussion revolves around the correct notation for factorials, specifically in the context of a series involving terms like 5*10*15*...*(5n). Participants explore whether this should be expressed as 5n!, (5n)!, or another form, and they consider the implications of these notations.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant suggests that the series can be written as 5n! and attempts to justify this by expanding it to 5(1*2*3*4*...*n).
  • Another participant corrects the misunderstanding about distribution in multiplication and proposes that the correct notation might be (5n)!, referencing the concept of quintuple factorial.
  • A different participant reiterates the quintuple factorial idea and provides a definition of double factorial for context.
  • Another participant proposes that the series can be expressed as 5^n * n!, explaining that each factor in the series contributes a factor of 5.
  • One participant later confirms that the correct notation is indeed 5n * n!, having received clarification from a tutor.

Areas of Agreement / Disagreement

Participants express differing views on the correct notation, with no consensus reached. Some support the idea of 5n! while others argue for (5n)! or 5^n * n!. The discussion remains unresolved regarding the preferred notation.

Contextual Notes

There are unresolved assumptions regarding the definitions and properties of factorials, particularly in relation to the proposed notations and their implications.

Drakkith
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I just have a quick question on how to write the notation for a factorial. I have a series with a factorial of 5*10*15*...*(5n) in it. Is this written as 5n!, as (5n)!, or something else? I'm pretty sure it's 5n!, as I've written 5n! out as 5(1*2*3*4*...*n), which when you distribute the 5 appears to come out as (5*10*15*...*5n), but I just wasn't sure if I'd broken some math rule somewhere.

Also, if it is 5n! and not (5n)!, can (5n)! be easily expressed in a form similar to (1*2*3*...*n)?

Thank you!
 
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Drakkith said:
which when you distribute the 5 appears to come out as (5*10*15*...*5n)

Multiplication doesn't distribute over multiplication.

I think you're looking for a quintuple factorial, i.e. ##(5n)!##. For instance, the double factorial is defined as $$(n)!=n \cdot (n-2) \cdot (n-4) ... 1$$

See here for more info: https://en.wikipedia.org/wiki/Factorial#Factorial-like_products_and_functions
 
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axmls said:
Multiplication doesn't distribute over multiplication.

Hah! Of course it doesn't! Silly me! :rolleyes:
@phinds You're rubbing off on me, old man!

axmls said:
I think you're looking for a quintuple factorial, i.e. (5n)!(5n)!(5n)!. For instance, the double factorial is defined as
(n)!=n⋅(n−2)⋅(n−4)...1(n)!=n⋅(n−2)⋅(n−4)...1​
(n)!=n \cdot (n-2) \cdot (n-4) ... 1

See here for more info: https://en.wikipedia.org/wiki/Factorial#Factorial-like_products_and_functions

Thanks! I'll look into it!
 
Drakkith said:
I just have a quick question on how to write the notation for a factorial. I have a series with a factorial of 5*10*15*...*(5n) in it
This would be ##5^n(1 * 2 * 3 * ... * n)## or ##5^n * n!##. Each of the n factors in the original expression has a factor of 5, which gives the ##5^n## part, and the remaining part is 1 * 2 * 3 * ... * n, or n!.
Drakkith said:
. Is this written as 5n!, as (5n)!, or something else? I'm pretty sure it's 5n!, as I've written 5n! out as 5(1*2*3*4*...*n), which when you distribute the 5 appears to come out as (5*10*15*...*5n), but I just wasn't sure if I'd broken some math rule somewhere.

Also, if it is 5n! and not (5n)!, can (5n)! be easily expressed in a form similar to (1*2*3*...*n)?

Thank you!
 
Mark44 said:
This would be 5n(1∗2∗3∗...∗n)5n(1∗2∗3∗...∗n)5^n(1 * 2 * 3 * ... * n) or 5n∗n!5n∗n!5^n * n!. Each of the n factors in the original expression has a factor of 5, which gives the 5n5n5^n part, and the remaining part is 1 * 2 * 3 * ... * n, or n!.

Gah! Somehow I missed the notification that you replied last night, Mark. I was just about to post the correct notation, which is 5nn!. Just got help from a tutor here on campus who figured it out. It all makes perfect sense now! :biggrin:
 
All these exclamation marks . . . everyone is so excited! :woot:
 

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