Maclaurin series for $f(x) = \frac{1}{1+x+x^2}$ I need to get the Maclaurin series and its radius of the convergence for  $f(x) = \dfrac{1}{1+x+x^2}$. I tried to do it manually, with getting the derivatives, but I gave up after some time, because I thought there had to be a better way to solve this. Could anyone help? Thanks in advance!

Note that, if $\lvert x\rvert<1$,\begin{align}\frac1{1+x+x^2}&=\frac{1-x}{(1+x+x^2)(1-x)}\\&=\frac{1-x}{1-x^3}\\&=(1-x)\times(1+x^3+x^6+x^9+\cdots)\\&=1-x+x^3-x^4+x^6-x^7+x^9-x^{10}+\cdots\end{align}
