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:
 
 2. Let's take the denominator and find the roots:
 
 
 3. The roots are  and the distance from the origin is .
 Therefore, the answer is: 

The Hamilton–Rosberg rivalry was a Formula One rivalry between British racing driver Lewis Hamilton and German racing driver Nico Rosberg. The rivalry was most prevalent during their four years as team-mates at Mercedes from 2013–2016, a period in which the two drivers dominated the sport. The pair's relationship became strained and, at times, led to volatile confrontations on and off the track, with the duo being threatened with suspension at the height of their rivalry.[1][2] It has been compared to the Prost–Senna rivalry.[3][4][5]

Lewis Hamilton (left) and Nico Rosberg (right) with Mercedes at the 2016 Malaysian Grand Prix

As teammates, Hamilton and Rosberg won 54 of 78 races over four seasons. Hamilton had 32 victories, 55 podium finishes and qualified ahead of Rosberg 42 times. Rosberg had 22 victories, 50 podium finishes and qualified ahead of Hamilton 36 times. During this period, Hamilton won the Formula One World Championship title twice, and Rosberg won the title once.[6]