# Power series representation

• September 23rd 2010, 07:22 AM
Webby
Power series representation
Hi I assume this question is quite simple, but I am just not able to crack it.
So I have to find the interval and radius of convergence for the function f(x). I am completely stumped as to how I can transform this into power series representation. All I can think of so far is saying that f(x) = d/dx(some nasty artan function). Is it possible to represent the function, as partial fractions?

f(x) = 5/(2+8(x-1)^2)

All help greatly appreciated.
• September 23rd 2010, 07:32 AM
chisigma
For $|x-1|<\frac{1}{2}$ is...

$\displaystyle f(x)= \frac{5}{2+8\ (x-1)^{2}} = \frac{5}{2}\ \frac{1}{1+4\ (x-1)^{2}} = \frac{5}{2} \ \{1-4\ (x-1)^{2} + 16\ (x-1)^{4} - 64\ (x-1)^{6} +...\}$

Kind regards

$\chi$ $\sigma$