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x^3

Sum of series x^3



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The solution

You have entered [src]
  oo    
 ___    
 \  `   
  \    3
  /   x 
 /__,   
x = 1   
$$\sum_{x=1}^{\infty} x^{3}$$
Sum(x^3, (x, 1, oo))
The radius of convergence of the power series
Given number:
$$x^{3}$$
It is a series of species
$$a_{x} \left(c x - x_{0}\right)^{d x}$$
- power series.
The radius of convergence of a power series can be calculated by the formula:
$$R^{d} = \frac{x_{0} + \lim_{x \to \infty} \left|{\frac{a_{x}}{a_{x + 1}}}\right|}{c}$$
In this case
$$a_{x} = x^{3}$$
and
$$x_{0} = 0$$
,
$$d = 0$$
,
$$c = 1$$
then
$$1 = \lim_{x \to \infty}\left(\frac{x^{3}}{\left(x + 1\right)^{3}}\right)$$
Let's take the limit
we find
True

False
The rate of convergence of the power series
The answer [src]
oo
$$\infty$$
oo
Numerical answer
The series diverges
The graph
Sum of series x^3

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