Binomial Expansion

  • Thread starter brunie
  • Start date
  • #1
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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?
 

Answers and Replies

  • #2
Dick
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x doesn't drop out of that expression. The power is x^(2007-2*k).
 
  • #3
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so
(2x)^2007-k isnt equivalent to (2)^2007-k * x^2007-k ??
 
  • #4
Dick
Science Advisor
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Sure it is. But x^(2007-k)*(1/x)^k=x^(2007-2*k).
 
  • #5
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ok yes that makes sense
thanks for ur help
 

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