
Taylor Series
Directions: Find the Taylor series for $\displaystyle f(x)$ centered at the given value of a. [Assume that f has a power series expansion. Do not show that $\displaystyle R_{n}(x)\rightarrow 0.$]
Problem:
$\displaystyle f(x)=\frac{1}{\sqrt{x}}, a=9$
The problem am having, or maybe i am confused, is when i start to list out the derivatives
$\displaystyle f(x)=\frac{1}{\sqrt{x}}$
$\displaystyle f'(x)=\frac{1}{2}x^{\frac{3}{2}}$
$\displaystyle f''(x)=\frac{3}{4}x^{\frac{5}{2}}$
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 34 terms of the taylor series?
Thanks

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.