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Finding a term in a binomial expnasion

  1. Mar 7, 2010 #1
    1. The problem statement, all variables and given/known data

    Find the term in the expansion of (x-(2/x^2))^14 which is of the form constant/x.



    3. The attempt at a solution
    I have worked out the general expression. (14|r) x^14-r * (-2/x^2)^r

    However I can only work out this problem by trial and error. I know that in this case r=5, however I didn't solve it by equation. What equation would I need to construct to get this answer r=5? I know that for the answer to be constant/x the power of x on the denominator can only be 1 greater than the power of x on the numerator.

    How do I construct an equation with r to solve this?

    Thanks
     
  2. jcsd
  3. Mar 7, 2010 #2

    Dick

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    (-2)/(x^2)^r=(-2)/x^(2r). And, just as you said, 14-r should be one less than 2r. Can you set up the equation from there?
     
  4. Mar 7, 2010 #3
    haha oh dear. bit of a facepalm moment.

    14-r=2r-1

    solve to get r=5

    I never thought of just putting 2r-1.

    Thanks for getting that out of me!
     
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