What is the radius of convergence of the maclaurin series (2x)/(1+x^2)?
Accepted Solution
A:
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]