Find the Maclaurin series of f(x) Find the Maclaurin series of $f(x)=\dfrac{1}{1+x+x^2}$ and the radius of convergence of the series.
I can't solve this problem.

A grneral method:
Maclaurin series: $f(x)=f(0)+f^{'}(0)x+\ldots+\frac{f^{(n)}(0)}{n!}x^n+\ldots $ 
Denote $a_n=\frac{f^{(n)}(0)}{n!}$, using Leibniz's rule,
$$
(1+x+x^2)f(x)=1 \Rightarrow (1+x+x^2)f^{(n)}+{n\choose 1}(1+2x)f^{(n-1)}+{n\choose 2}\cdot2\cdot f^{(n-2)}=0
$$
Let $x=0$, we obtain
$$
f^{(n)}(0)+nf^{(n-1)}(0)+n(n-1)f^{(n-2)}(0)=0
$$
which is equivalent to
$$
\frac{f^{(n)}(0)}{n!}+\frac{f^{(n-1)}(0)}{(n-1)!}+\frac{f^{(n-2)}(0)}{(n-2)!}=0
$$
Hence $a_n=-(a_{n-1}+a_{n-2})$, and $a_0=1,a_1=-1$. Now you know the Maclaurin series.
