The function $f(x) = \frac{3}{(1 + 3 x)^2}$ is represented as a power series:
$$f(x) = \sum_{n=0}^\infty c_n x^n$$
Find the first few coefficients in the power series.
$c_0 =$
$c_1 =$
$c_2 =$
$c_3 =$
$c_4 =$

Find the radius of convergence $R$ of the series.
$R =$ .