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(k^3-k^2)
Sum of series/ (k^3-k^2)

Sum of series (k^3-k^2)


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The solution

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k = 1
$$\sum_{k=1}^{\infty} \left(k^{3} - k^{2}\right)$$ 
Sum(k^3 - k^2, (k, 1, oo))
The radius of convergence of the power series
Given number:
$$k^{3} - k^{2}$$
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
$$a_{k} = k^{3} - k^{2}$$
and
$$x_{0} = 0$$
,
$$d = 0$$
,
$$c = 1$$
then
$$1 = \lim_{k \to \infty} \left|{\frac{k^{3} - k^{2}}{\left(k + 1\right)^{3} - \left(k + 1\right)^{2}}}\right|$$
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 (k^3-k^2)

    Examples of finding the sum of a series

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