Respuesta :

carlosego
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]

The radius of convergence of the maclaurin series is 1 unit.

It is given that maclaurin series  [tex]\rm \frac{2x}{(1+x^2)}[/tex]

It is required to find the radius of the convergence of the maclaurin series.

What is maclaurin series?

It is defined as the expansion of a function that provide the approximation of the given function at any point of function.

We have:

[tex]\rm \frac{2x}{(1+x^2)}[/tex]

To find the radius of convergence of the maclaurin series, we must find the roots of denominator hence:

[tex]\rm 1+x^2= 0\\\\\rm x^2 = -1\\\\[/tex]

From the complex number: the roots are imaginary:

[tex]\rm x_1 = i\\x_2 = -i[/tex]

i is the iota

and the distance from the origin (0,0) is 1.

Thus, the radius of convergence of the maclaurin series is 1 unit.

Learn more about the maclaurin series:

https://brainly.com/question/24188694

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