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  • Sum of series:
  • (2^n+(-1)^n)/5^n (2^n+(-1)^n)/5^n
  • 1/n^n 1/n^n
  • (-1/2)^n (-1/2)^n
  • n^2*sin(5/(3^n)) n^2*sin(5/(3^n))

  • Identical expressions

  • arctg(x^ three / two)
  • arctg(x cubed divide by 2)
  • arctg(x to the power of three divide by two)
  • arctg(x3/2)
  • arctgx3/2
  • arctg(x³/2)
  • arctg(x to the power of 3/2)
  • arctgx^3/2
  • arctg(x^3 divide by 2)
Sum of series/ arctg(x^3/2)

Sum of series arctg(x^3/2)


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The solution

You have entered [src] 
  oo          
____          
\   `         
 \        / 3\
  \       |x |
  /   atan|--|
 /        \2 /
/___,         
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
$$1 = \lim_{n \to \infty} 1$$
Let's take the limit
we find
True

False
The answer [src] 
       / 3\
       |x |
oo*atan|--|
       \2 /
$$\infty \operatorname{atan}{\left(\frac{x^{3}}{2} \right)}$$ 
oo*atan(x^3/2)

    Examples of finding the sum of a series

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