Thus, the general formula is

n $=0$

$$

$.$

Step $5$

Using the Ratio Test to find the radius of convergence, we have

lim$$n $$ $$

an $+1$an

$=$lim$$n $$ $$

$$

$(2$n$)!532$nx$2$n$(2$n $+2)!$

$.$

Step $6$

Simplifying, we get

lim$$n $$ $$

$9$

$|$x$2|=$

$.$