# Taylor Series

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• April 5th 2009, 06:07 PM
mortalapeman
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
• April 5th 2009, 08:15 PM
matheagle
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.