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Factorials homework help

  1. Jun 2, 2009 #1
    1. The problem statement, all variables and given/known data
    Hi! I need to find ratio (2n+1)!/(2n+3)! for interval of convergence calculation.


    2. Relevant equations
    5! = 1*2*3*4*5


    3. The attempt at a solution

    i have no idea where to start since i have never dealt with factorials before.. if you just show me some kind off factorial property i can use ill be able to figure it out. wikipedia didnt help.
     
  2. jcsd
  3. Jun 2, 2009 #2
    Re: Factorials!

    5! = 5*4*3*2*1 and 4! = 4*3*2*1, so
    5! = 5*4!
    5! = 5*4*3!

    n! = n*(n -1)!
    n! = n*(n-1)*(n-2)!
    and more generally, n! = n*(n-1)*(n-2)...3*2*1

    See if you can break down (2n + 1)! and (2n + 3)! so you can cancel something.
     
  4. Jun 2, 2009 #3
    Re: Factorials!

    oh.. awesome thanks a lot.
    after very long thing of expanding that i got 1/ (2n+3)
     
  5. Jun 2, 2009 #4
    Re: Factorials!

    Your answer is not quite right, and obtaining the correct one should not take much expanding. You only need to apply the identity n! = n*(n-1)*(n-2)! to the denominator.
     
  6. Jun 2, 2009 #5
    Re: Factorials!

    (2n+3)=(2n+3)*(2(n-1)+1)! = 2n+3)*(2n-2+3)! =(2n+3)(2n+1)! ||| (2n+1)! cancels and im left with 1/(2n+3)
     
  7. Jun 2, 2009 #6
    Re: Factorials!

    You should have (2n+2) somewhere; looks like you factored out the 2 and then it got lost...
     
  8. Jun 14, 2011 #7
    Re: Factorials!

    I think it is 1/(4n^2+10n+6)
     
  9. Jun 14, 2011 #8
    Re: Factorials!

    Like Bohrok said,

    5! = 5*4*3*2*1 and 4! = 4*3*2*1, so
    5! = 5*4!
    5! = 5*4*3!

    Use this logic to simplify your question. :smile:
    It would go like this:-

    [tex]\frac{(2n+1)!}{(2n+3)(2n+2)(2n+1)!}[/tex]

    Now cancel out (2n+1)! and you get:-

    [tex]\frac{1}{(2n+3)(2n+2)}[/tex]

    Done !! :wink:
     
  10. Jun 14, 2011 #9
    Re: Factorials!

    Umm... that can be simplified to 1/(4n^2+10n+6). From this, we can see that when and only when n=-1 or -1.5, (2n+1)!/(2n+3)!=infinity
     
    Last edited: Jun 14, 2011
  11. Jun 14, 2011 #10
    Re: Factorials!

    What did queensu mean by "for interval of convergence calculation"?
     
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