What is the radius of convergence of the maclaurin series (2x)/(1+x^2)?

To solve this problem you must apply the proccedure shown below:
 1. You have to find the radius of convergence of the following Maclaurin series:
 [tex](2x)/(1+ x^{2} ) [/tex]
 2. Let's take the denominator and find the roots:
 [tex]1+ x^{2} =0[/tex]
 [tex] x^{2} =-1 \\ x= \sqrt{-1} \\ x1=i \\ x2=-i[/tex]
 3. The roots are [tex]x1=i \\ x2=-i[/tex] and the distance from the origin is [tex]1[/tex].
 Therefore, the answer is: [tex]1[/tex]