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Sum of series x^2*arctg(x^2/4)

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  oo             
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  /   x *atan|--|
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n = 1

\sum_{n=1}^{\infty} x^{2} \operatorname{atan}{\left(\frac{x^{2}}{4} \right)}

Sum(x^2*atan(x^2/4), (n, 1, oo))

The radius of convergence of the power series

Given number:

x^{2} \operatorname{atan}{\left(\frac{x^{2}}{4} \right)}

It is a series of species

a_{n} \left(c x - x_{0}\right)^{d n}

- power series.
The radius of convergence of a power series can be calculated by the formula:

R^{d} = \frac{x_{0} + \lim_{n \to \infty} \left|{\frac{a_{n}}{a_{n + 1}}}\right|}{c}

In this case

a_{n} = x^{2} \operatorname{atan}{\left(\frac{x^{2}}{4} \right)}

and

x_{0} = 0

d = 0

c = 1

then

1 = \lim_{n \to \infty} 1

True

False

The answer [src]

          / 2\
    2     |x |
oo*x *atan|--|
          \4 /

\infty x^{2} \operatorname{atan}{\left(\frac{x^{2}}{4} \right)}

oo*x^2*atan(x^2/4)