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Math Help - binomials

  1. #1
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    binomials

    I have been set this question and don't know wherto begin to get powers from..

    Show that,, \frac{(2n)!}{n!}=2^n.1.3.5...(2n-1)
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  2. #2
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    \left[ {2n} \right]! = \left( {2n} \right)\left( {2n - 1} \right)\left( {2n - 2} \right)\left( {2n - 3} \right)\left( {2n - 4} \right) \cdots (4)(3)(2)(1)
    \left[ {2n} \right]! = 2\left( n \right)\left( {2n - 1} \right)2\left( {n - 1} \right)\left( {2n - 3} \right)2\left( {n - 2} \right) \cdots 2(2)(3)2(1)(1), factor out 2's.
    \left[ {2n} \right]! = 2^n \left( n \right)\left( {2n - 1} \right)\left( {n - 1} \right)\left( {2n - 3} \right)\left( {n - 2} \right) \cdots (2)(3)(1)(1), there are n 2's. Do you see a factor of n!?
    \left[ {2n} \right]! = 2^n \left( {2n - 1} \right)\left( {2n - 3} \right)\left( {n - 2} \right) \cdots (3)(1)(n!)
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  3. #3
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    where did the n from your 3rd line come from?
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  4. #4
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    Quote Originally Posted by oxrigby View Post
    where did the n from your 3rd line come from?
    2 times itself n times is 2^n.
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  5. #5
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    got it
    Last edited by oxrigby; October 2nd 2008 at 02:35 PM. Reason: got it
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