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Math Help - Taylor Series

  1. #1
    Junior Member
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    Taylor Series

    Directions: Find the Taylor series for f(x) centered at the given value of a. [Assume that f has a power series expansion. Do not show that R_{n}(x)\rightarrow 0.]

    Problem:

    f(x)=\frac{1}{\sqrt{x}}, a=9

    The problem am having, or maybe i am confused, is when i start to list out the derivatives

    f(x)=\frac{1}{\sqrt{x}}
    f'(x)=-\frac{1}{2}x^{-\frac{3}{2}}
    f''(x)=\frac{3}{4}x^{-\frac{5}{2}}

    and so on, the functions become difficult to get a value for that i can use to recognize a pattern. I am taking the derivative correctly right? If so can someone help me list the first 3-4 terms of the taylor series?

    Thanks
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  2. #2
    MHF Contributor matheagle's Avatar
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    are you asking for the sequence of coefficients?

    as in (1)(3)(5)(7)... over powers of 2?

    There is a nice trick to find the product of odd numbers.
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