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Math Help - Remainder of a Taylor Series.

  1. #1
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    Arrow Remainder of a Taylor Series.

    Could someone give me a quick run through on how to evaluate the Remainder term of a Taylor series?

    I'm supposed to calculate the 4th Taylor polynomial of:

    \sqrt{1+x}

    I did this and got:

    T_{4}~=~\frac{x^{3}}{512}-\frac{17x^{2}}{512}+\frac{203x}{512}+\frac{541}{51  2}

    And I found that the nth derivative of this function can be given by:

    f^{\left(n\right)}\left(x\right)~=~\left(-1\right)^{\left(n-1\right)}\frac{\left(2n-3\right)!!}{2^{n}\left(x+1\right)^{\frac{2n-1}{2}}}

    I'm not 100% sure how to calculate the remainder now.
    Last edited by leverin4; May 4th 2009 at 05:05 PM.
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  2. #2
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    I made a small change, it used to say (n-5)!!

    Now it is (n-3)!! as it should be.
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