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(n^2-3n-18)
Sum of series/ (n^2-3n-18)

Sum of series (n^2-3n-18)


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The solution

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n = 1
$$\sum_{n=1}^{\infty} \left(\left(n^{2} - 3 n\right) - 18\right)$$ 
Sum(n^2 - 3*n - 18, (n, 1, oo))
The radius of convergence of the power series
Given number:
$$\left(n^{2} - 3 n\right) - 18$$
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
$$a_{n} = n^{2} - 3 n - 18$$
and
$$x_{0} = 0$$
,
$$d = 0$$
,
$$c = 1$$
then
$$1 = \lim_{n \to \infty} \left|{\frac{- n^{2} + 3 n + 18}{3 n - \left(n + 1\right)^{2} + 21}}\right|$$
Let's take the limit
we find
True

False
The rate of convergence of the power series
Numerical answer
The series diverges
The graph
Sum of series (n^2-3n-18)

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