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Homework Help: Does ( 2(n+1))! = 2!(n+1)! ) ?

  1. Jan 28, 2008 #1
    1. The problem statement, all variables and given/known data

    Just a quick on - this is a little bit out of a bigger question.

    Does ( 2(n+1))! = 2!(n+1)! ) ?

    Do you know of anywhere on the net where i can find factorial properties?

    Thanks
     
  2. jcsd
  3. Jan 28, 2008 #2
    No they are not equal.
    If you write out those factorials explicitly you should see why
    See http://en.wikipedia.org/wiki/Factorials" [Broken] if you want more info
     
    Last edited by a moderator: May 3, 2017
  4. Jan 28, 2008 #3

    HallsofIvy

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    Did you TRY anything at all? If n= 1, (2(n+1))!= (2(2))!= 4!= 24 while 2!(n+1)! = 2(2)= 4. You can't get simpler than that.
     
  5. Jan 28, 2008 #4
    yeah - i did after i posted - too hasty - sorry
     
  6. Jan 29, 2008 #5
    so im meant to calcultae the radius of convergence and i have got to

    ... lZl(2(n+1))!/(2n)!(n+1)^2


    what shall i do with the (2(n+1))!/(2n)! ?
     
  7. Jan 29, 2008 #6

    HallsofIvy

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    (2n)!= (2n)(2n-1)... (n+1)! so 2(n+1)!/(2n)!= 2/[(2n)(2n-1)...(n+2)!]. what happens to that as n goes to infinity?
     
  8. Dec 29, 2009 #7
    Re: Factorials

    Hi, similar kind of question.

    Find all solutions in positive integers a; b; c to the equation
    a!b! = a! + b! + c!

    I have rearranged and got (a!-1)(b!-1) = c!+1

    And the only solutions I can find are a=3 b=3 c=4 but I can't be sure that they are the only ones. How would I go about finding other solutions?
     
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