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Math Help - Factorials, find the 58th term

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    Factorials, find the 58th term

    find the 58th term in the expansion of (2x-3y)^100
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  2. #2
    Behold, the power of SARDINES!
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    The binomial theorem...

    Quote Originally Posted by cm3pyro View Post
    find the 58th term in the expansion of (2x-3y)^100
    we will need this formula
    {n\choose k}=\frac{n!}{k!(n-k)!}


    From the Binomial Therom this will generate the k+1 th term.

    {{n}\choose {k}}a^{n-k}b^k

    so we need n=100 k=57
    a=2x and b=-3y

    evaluating at the above values gives




    {{n}\choose {k}}a^{n-k}b^k=\frac{100!}{57!(100-57)!}(2x)^{100-57}(-3y)^{57}

    I hope this helps
    Last edited by TheEmptySet; February 24th 2008 at 11:12 AM. Reason: Left out a y in the -3y term
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  3. #3
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    (-3)^57

    (-3y)^57, correct?
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  4. #4
    Behold, the power of SARDINES!
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    Yes sorry for the typo.
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