Answer
$4$
Work Step by Step
The radius of convergence of a power series represented by $\dfrac{A(x)}{B(x)}$ can be defined as the distance from $min(|x_0-y|)$, where y is root of $B(x)$, that is, $B(y)=0$.
We have: $\dfrac{A(x)}{B(x)}=\dfrac{x}{(x^2+4x+13)(x-3)}; x_0=-1$
This implies that the root of $B(x)=(x^2+4x+13)(x-3)=0 \implies x =-2 \pm 3i, 3$
So, the radius of convergence is $R=min|-3-1|=4$
