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Help with binomial theorem

  1. Oct 28, 2009 #1
    1. The problem statement, all variables and given/known data

    prove that ([tex]\stackrel{2n}{n}[/tex]) is even when n [tex]\geq1[/tex]

    2. Relevant equations

    as a hint they gave me this identity:
    [tex]\stackrel{n}{k}[/tex]= (n/k)([tex]\stackrel{n-1}{k-1}[/tex])

    3. The attempt at a solution

    by using that identity i got:

    ([tex]\stackrel{2n}{n}[/tex]) = (2n/n) ([tex]\stackrel{2n-1}{n-1}[/tex])
    = (2) ([tex]\stackrel{2n-1}{n-1}[/tex])

    i thought anything multiplied by 2 is an even number. but then again this is discrete math. how would i inductively show that this is true?
     
  2. jcsd
  3. Oct 28, 2009 #2

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    That's pretty much it. The definition of "even number" is that it is of the form 2k for some integer k. Do you already know that [itex]\left(\begin{array}{c}n\\2i\end{array}\right)[/itex] is always an integer?
     
  4. Oct 28, 2009 #3
    oh yeah! I forgot about that! thanks!
     
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