1. ## Power series help

$\displaystyle f(x)=\frac{1}{4+x^2}$
a)write the first four terms and general term for the power series expansion of f about x=0
b)find the radius of convergence of the series found in part a)

Sorry but i don't really know how to do power series problems... I know
$\displaystyle \sum_{0}^{\infty}C_{n}X^n=C_{0}+C_{1}X+C_{2}X^2...$ but i don't really know what this means. Any Help?

2. Is...

$\displaystyle f(x)= \frac{1}{4}\cdot \frac{1}{1+(\frac{x}{2})^{2}}$ (1)

... so that we can expand f(*) as 'geometric series' ...

$\displaystyle f(x) = \frac{1}{4}\cdot \sum_{n=0}^{\infty} (-1)^{n}\cdot (\frac{x}{2})^{2n}$ (2)

... that converges for $\displaystyle |x|<2$...

Kind regards

$\displaystyle \chi$ $\displaystyle \sigma$
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