# Representing functions as power series and finding $c_0,c_1,c_2$...

I have a problem with representing functions as power series: question http://puu.sh/hvUGb/b48c3a9217.png

I was trying to find $c_0$, $c_1$, $c_2$, ... and the Radius of Convergence but I'm not sure how to do this, I'm a bit lost here could someone give me some advice or help on this?

• Do you know the power series expansion of $1/(1-y)$? Can you modify this somehow to cover the function you're given? Apr 30, 2015 at 4:11

Hint. One may recall that $$\frac{1}{1-q}=\sum_{n=0}^{+\infty} q^n,\quad |q|<1.$$ Here you may put $q=8x$ and the radius of convergence is obtained from $x$ such that $|8x|<1$.