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Sum of series arctg(x^3/2)

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  oo          
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\   `         
 \        / 3\
  \       |x |
  /   atan|--|
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/___,         
n = 1

\sum_{n=1}^{\infty} \operatorname{atan}{\left(\frac{x^{3}}{2} \right)}

Sum(atan(x^3/2), (n, 1, oo))

The radius of convergence of the power series

Given number:

\operatorname{atan}{\left(\frac{x^{3}}{2} \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} = \operatorname{atan}{\left(\frac{x^{3}}{2} \right)}

and

x_{0} = 0

d = 0

c = 1

then

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

True

False

The answer [src]

       / 3\
       |x |
oo*atan|--|
       \2 /

\infty \operatorname{atan}{\left(\frac{x^{3}}{2} \right)}

oo*atan(x^3/2)