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N /n! = ?

  1. Jan 28, 2010 #1
    n!!/n! = ?

    Hi, I have a quick question that's been bugging me: is there an easy simplification of (n!!)/(n!)? And how is is demonstrated?
     
  2. jcsd
  3. Jan 28, 2010 #2
    Re: n!!/n! = ?

    Yup. Depends on whether n is even or odd.

    Try working it out. The answer will come in terms of another double factorial.

    EDIT: My bad, it does not depend on whether n is even or odd.
     
    Last edited: Jan 28, 2010
  4. Jan 28, 2010 #3
    Re: n!!/n! = ?

    I can hardly call it a simplication if it has another double factorial. I would just say it's another way to write it. It's equivalent.

    The obvious answer to something that is equivalent...

    (n!!-1)!
     
  5. Jan 28, 2010 #4
    Re: n!!/n! = ?

    Why? We have a factorial and a double factorial and we can reduce it to just a double factorial.

    That sounds like simplification to me.
     
  6. Jan 29, 2010 #5
    Re: n!!/n! = ?

    :rofl:
    I laughed when I looked at your original question because I thought to myself:

    [tex]\frac{n!!}{n!} = ?[/tex] ... that can't be; where does the "?" come from?

    It should be [tex]\frac{n!!}{n!} = ![/tex] since the "n!" cancels out.

    Like this: [tex]\frac{n!!}{n!} = \frac{(n!)!}{n!} = \frac{n!}{n!}\times ! = 1\times ! = ![/tex] :rolleyes:
     
  7. Jan 29, 2010 #6
    Re: n!!/n! = ?

    In differential equations class, they had...

    [tex]x = \frac{dy}{dx}[/tex]

    The student cancelled the d's, and then multiplied both sides by x and added "+C". That's [itex]y = x^2 + C[/itex]. Argued his answer was correct and was only missing an insignificant coeficient and should get full marks.
     
  8. Jan 29, 2010 #7
    Re: n!!/n! = ?

    Im not a mathemagician. But you could use Stirling's approximation if you assume large n.
     
  9. Jan 29, 2010 #8

    Mark44

    Staff: Mentor

    Re: n!!/n! = ?

    That's like
    [tex]\frac{sin x}{n}= 6[/tex]
     
  10. Jan 29, 2010 #9
    Re: n!!/n! = ?

    Good one! (It took me a while, but I got it!)
     
  11. Jan 29, 2010 #10
    Re: n!!/n! = ?

    I know a guy who actually did that on a Calculus Preparedness Exam for our physics class. Wherever there was d/dx, he would just cancel the d's and divide by x.
     
  12. Jan 29, 2010 #11

    Char. Limit

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    Re: n!!/n! = ?

    Lol, it even kind of works for polynomials, if you commonly ignore coefficients...
     
  13. Jan 29, 2010 #12

    uart

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    Re: n!!/n! = ?

    Actually it's [itex](n! - 1)![/itex]. You slipped in an extra factorial there. :)
     
  14. Jan 29, 2010 #13
    Re: n!!/n! = ?

    Hence why the student kept arguing.
     
  15. Jan 29, 2010 #14

    Char. Limit

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    Re: n!!/n! = ?

    I would hardly call any coefficient insignificant, though.

    What's the difference between [tex]x^3[/tex] and [tex]100x^3[/tex]? Only an insignificant coefficient that changes the answer by a factor of 2.
     
  16. Jan 29, 2010 #15
    Re: n!!/n! = ?

    that is in the simplest possible form
     
  17. Jan 29, 2010 #16
    Re: n!!/n! = ?

    I mean, you have one variable and 3 of the same operators. What are you hoping for?
     
  18. Jan 29, 2010 #17
    Re: n!!/n! = ?

    n!!=n(n-2)(n-4).... right? I get 1/((n-1)!!) just by writing it out and cancelling out.
     
  19. Jan 29, 2010 #18
    Re: n!!/n! = ?

    Good job. : )
     
  20. Jan 29, 2010 #19
    Re: n!!/n! = ?

    OH!

    I was thinking (n!)!.
     
  21. Jan 30, 2010 #20

    uart

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    Re: n!!/n! = ?

    I thought the same thing here Norm. Maybe the OP could have explained it's meaning since it's not such a common symbol and easily confused.

    Also I must say that I find "double factorial" a very unintuitive name for that function. It should be called "half factorial" IMHO.
     
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