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(1)/5*n-4*5*n+1
Sum of series/ (1)/5*n-4*5*n+1

Sum of series (1)/5*n-4*5*n+1


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The solution

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  )   (0.2*n - 20*n + 1)
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n = 1
$$\sum_{n=1}^{\infty} \left(\left(- 20 n + 0.2 n\right) + 1\right)$$ 
Sum(0.2*n - 20*n + 1, (n, 1, oo))
The radius of convergence of the power series
Given number:
$$\left(- 20 n + 0.2 n\right) + 1$$
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
$$a_{n} = 1 - 19.8 n$$
and
$$x_{0} = 0$$
,
$$d = 0$$
,
$$c = 1$$
then
$$1 = \lim_{n \to \infty}\left(\frac{\left|{19.8 n - 1}\right|}{19.8 n + 18.8}\right)$$
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 (1)/5*n-4*5*n+1

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