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Simplifying a Factorial

  1. Jan 25, 2014 #1
    1. The problem statement, all variables and given/known data

    $$ \frac{(2n-1)!}{(2n+1)!} $$

    How do you simplify this factorial?
     
  2. jcsd
  3. Jan 25, 2014 #2

    vanhees71

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    Science Advisor
    2016 Award

    Just write out the factorials. Then you'll see immediately how to simplify the expression.
     
  4. Jan 25, 2014 #3
    I cannot tell from writing them out.
    $$\frac{1*3*5*7*9...(2n-1)!}{3*5*7*9*11...(2n+1)!} $$
    Please explain.


    Edit:
    Nvm, I understand. Thank you!

    $$\frac{(2n-1)!}{(2n+1)!} = \frac{(2n-1)*(2n-2)*(2n-3)*(2n-4)...2*1}{(2n+1)*(2n)*(2n-1)*(2n-2)...2*1} $$
    $$ = \frac{1}{(2n)*(2n+1)} $$

    or

    $$\frac{(2n-1)!}{(2n+1)!} = \frac{(2n-1)!}{(2n+1)*(2n)*(2n-1)!} $$
    $$ = \frac{1}{(2n+1)*(2n)} $$
     
    Last edited: Jan 25, 2014
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