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Binomial Expansion

  1. Mar 24, 2007 #1
    Hi,
    Im having some troubles with this binomial expansion...

    Determine the coefficient of x^k, where k is any integer, in the expansion of (2x - 1/x)^2007.

    I figured it would just be
    C(2007,k) * (2x)^2007-k * (-1/x)^k
    = C(2007,k) * (2)^2007-k * x^2007-k * (-1/x)^k

    therefore the coefficient would only be the constant terms with no variables

    but when i tried it on a smaller scale (ie small exponent), and factored it out, the equation i found doesnt work

    i think it is due to the common variable x

    anyone kno what to do?
     
  2. jcsd
  3. Mar 24, 2007 #2

    Dick

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    x doesn't drop out of that expression. The power is x^(2007-2*k).
     
  4. Mar 24, 2007 #3
    so
    (2x)^2007-k isnt equivalent to (2)^2007-k * x^2007-k ??
     
  5. Mar 24, 2007 #4

    Dick

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    Sure it is. But x^(2007-k)*(1/x)^k=x^(2007-2*k).
     
  6. Mar 24, 2007 #5
    ok yes that makes sense
    thanks for ur help
     
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