Find Power Series representation of the function $f(x) = {x\over 2x^2 + 1}$? 
Find Power Series representation of the function $f(x) = \dfrac x{2x^2 + 1}$?

I'm not sure how to tackle this...I'm supposed to find interval of convergence. 

A variation: From the geometric series
\begin{align*}
\frac{1}{1-x}=\sum_{n=0}^\infty x^n\qquad\qquad\qquad |x|<1
\end{align*}

we obtain
  \begin{align*}
\frac{x}{2x^2+1}&=\frac{x}{1-\left(-2x^2\right)}\\
&=x\sum_{n=0}^\infty (-2x^2)^n\qquad\qquad &|-2x^2|&<1\\
&=\sum_{n=0}^\infty (-2)^nx^{2n+1} &|x|&<\frac{1}{\sqrt{2}}\\
\end{align*}

