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I Notation for Factorials!

  1. Apr 27, 2016 #1

    Drakkith

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    Staff: Mentor

    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!
     
  2. jcsd
  3. Apr 27, 2016 #2
    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
     
  4. Apr 27, 2016 #3

    Drakkith

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

    Thanks! I'll look into it!
     
  5. Apr 28, 2016 #4

    Mark44

    Staff: Mentor

    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!.
     
  6. Apr 28, 2016 #5

    Drakkith

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    Staff: Mentor

    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:
     
  7. Apr 29, 2016 #6

    ProfuselyQuarky

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    2016 Award

    All these exclamation marks . . . everyone is so excited!!!! :woot:
     
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