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Homework Help: Binomial theorem proof

  1. Feb 11, 2012 #1
    1. The problem statement, all variables and given/known data

    Show that if the greatest term in the expansion of (1+x)2n is also the greatest coefficient, then x lies between n/n+1 and n+1/n.

    2. Relevant equations

    No idea.

    3. The attempt at a solution

    Don't know where to start.
     
  2. jcsd
  3. Feb 12, 2012 #2
    2n is obviously an even number, so your greatest coefficient occurs at the nth term. Use the binomial expansion to also find your (n-1)th and (n+1)th terms (their coefficients will be equal), plug in your given boundaries for x, and do a little algebra to show that at one of the boundaries the (n-1)th and nth terms are equal and at the other boundary the nth and (n+1)th terms are equal. Hopefully this leads you in the right direction.
     
  4. Feb 13, 2012 #3
    Thank You, it is clear now.
     
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