Sum of series k^3/

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  oo    
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  \    3
  /   k 
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k = 1

\sum_{k=1}^{\infty} k^{3}

Sum(k^3, (k, 1, oo))

The radius of convergence of the power series

Given number:

k^{3}

It is a series of species

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

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

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

In this case

a_{k} = k^{3}

and

x_{0} = 0

d = 0

c = 1

then

1 = \lim_{k \to \infty}\left(\frac{k^{3}}{\left(k + 1\right)^{3}}\right)

True

False

The rate of convergence of the power series

The answer [src]

oo

\infty

oo

Numerical answer

The series diverges

The graph