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Math Help - Maclaurin expansion

  1. #1
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    Maclaurin expansion

    Use known Maclaurin expansions to find the Maclaurin expansion, by adding, composing, differentiating, and so on.

    1/((1-x)^3)

    is the function I'm supposed to expand and I don't even know where to start. Thanks in advance!!!!
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  2. #2
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    MacLaurin expansion is f(0)+f'(0)x+\frac{f''(0)}{2!}x^{2}+\frac{f'''(0)x^  {3}}{3!}+.......+\frac{f^{n}(0)}{n!}x^{n}

    f(x)=\frac{1}{(1-x)^{3}}

    f'(x)=\frac{3}{(x-1)^{4}}

    f''(x)=\frac{-12}{(x-1)^{5}}

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    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

    f(0)=1

    f'(0)x=3x

    \frac{f''(0)}{2!}x^{2}=6x^{2}

    \frac{f'''(0)}{3!}x^{3}=10x^{3}

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    See the pattern.
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  3. #3
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    Thanks!!!!!

    I wasn't using the derivative correctly. Thanks again!!!


    Repped
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  4. #4
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    Quote Originally Posted by TreeMoney View Post
    Use known Maclaurin expansions to find the Maclaurin expansion, by adding, composing, differentiating, and so on.

    1/((1-x)^3)

    is the function I'm supposed to expand and I don't even know where to start. Thanks in advance!!!!
    Use the fact below and a known Maclaurin expansion:
    Attached Thumbnails Attached Thumbnails Maclaurin expansion-july3.gif  
    Last edited by curvature; July 16th 2007 at 08:04 PM.
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