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**mollymcf2009** Find the Taylor Series for f(x) centered at a=25. (assume f has a power series expansion)

$\displaystyle f(x) = \frac{1}{\sqrt{x}}$

I'm not going to type all these derivatives, but here are the 4th and nth:

$\displaystyle f^4(x) = (-\frac{1}{2})(-\frac{3}{2})(-\frac{5}{2})(-\frac{7}{2}) x^{-\frac{9}{2}}$

So, when I calculated my nth derivative, I got:

$\displaystyle f^n(25) = (-\frac{1}{2})(-\frac{3}{2})(-\frac{5}{2})(-\frac{7}{2}) (-\frac{9}{2})...-\frac{(2n+1)}{2}(25)^{2n+1}$

No idea....

EDIT: Do I need to use the binomial series here?