Question

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

Answer 1

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:
 $(2x)/(1+ x^{2} )$
 2. Let's take the denominator and find the roots:
 $1+ x^{2} =0$
 $x^{2} =-1 \\ x= \sqrt{-1} \\ x1=i \\ x2=-i$
 3. The roots are $x1=i \\ x2=-i$ and the distance from the origin is $1$.
 Therefore, the answer is: $1$