Answer
$\dfrac{9}{4}$
Work Step by Step
Let us apply the Ratio Test to the given series.
$\lim\limits_{n \to \infty} |\dfrac{a_{n+1}}{a_n}|=|\lim\limits_{n \to \infty} \dfrac{(2n+2)^2 \cdot x}{(3n+2)^2} | \\=|x| \lim\limits_{n \to \infty}\dfrac{ (2+\dfrac{2}{n})^2 }{3+\dfrac{2}{n}} \\=\dfrac{4}{9}|x|$
So, $\dfrac{4}{9}|x|| \lt 1 $
and $|x| \lt \dfrac{9}{4}$
The radius of convergence is: $\dfrac{9}{4}$
