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Math Help - Binomial theporem : Finding the Coefficient

  1. #1
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    Binomial theporem : Finding the Coefficient

    Me again.

    Got stuck on my last practice question and its because I have literally no idea what it is asking me.

    The question says:

    Find the coefficient of x^9in the expansion of (x-\frac{2}{x})^1^5

    I Literally have no clue. If someone could try and talk me through this id really appreciate it.
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  2. #2
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    The binomial theorem states that

    \displaystyle (a+b)^n=\sum_{k=0}^{n}\binom{n}{k}a^{k}b^{n-k}

    So in your case you want

    \displaystyle (x)^{k}\left( \frac{2}{x}\right)^{n-k}=(\text{some number})x^{9}

    Since we know that n=15 use this to solve for k and then find the coeffient.
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  3. #3
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    You want to solve this \dbinom{15}{k}\left(x^k\right) \left(\frac{-2}{x}\right)^{15-k}=\mathcal{C}x^9 .
    Find k~\&~\mathcal{C}.
    The answer is  \mathcal{C}
    Last edited by Plato; October 31st 2010 at 03:28 PM.
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    Sorry guys...

    At the risk of sounding thick: I really don't have a clue where to begin.
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  5. #5
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    Quote Originally Posted by Tauron View Post
    At the risk of sounding thick: I really don't have a clue where to begin.
    If x^k \left( {x^{k - 15} } \right) = x^9 then what is k~?
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  6. #6
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    12?
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  7. #7
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    Good for you!
    Now \mathcal{C}=\dbinom{15}{12}(-2)^{15-12}
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  8. #8
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    would the (15/12) be 2520?

    If I remember its something to do with the factorials and cancelling. Not sure if Im on the right lines though.
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  9. #9
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    I mean you no disrespect.
    But you have absolutely no business doing this question if you do not know that \dbinom{15}{12}=\dfrac{15!}{12!\cdot 3!}.
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  10. #10
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    Dont worry about it Plato! If it were my choice I wouldnt be doing these types of questions.

    Perhaps a bit of background might help. Im having to do a Maths course at University as it is a required credit to pass out this year. However, maths was not required to be on my course (English Lit!) and at no point have I ever sat a decent level of math before.

    Now if you could bear with me in the understanding that I was only introduced to the concept of a "factorial" and a "binomial expansion" in my last lecture then that would be appreciated!
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