I am working on the power series.
Here is the question
$$f(x)=\frac {9}{1+100x^2}$$ represented as a power series $$f(x) = \sum^{\infty}_{n=0}c_nx^n$$
I need to find $c_0,c_1,c_2,c_3,c_4,R$
I got this
$c_0=9$
$c_1=-90$
$c_2=1800$
$c_3=-54000$
$c_4=2160000$
$R= \frac {1}{10}$
I know that $c_{1-4}$ are wrong. I don't know why
I got the summation to be $$\sum^{\infty}_{n=0}9(-10x)^n$$ $$9-90x+900x^2-9000x^3+90000x^4$$
taking derivatives to find the $c_n$