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1/25n^2+15n-4
Sum of series/ 1/25n^2+15n-4

Sum of series 1/25n^2+15n-4


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The solution

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  oo                 
____                 
\   `                
 \    / 2           \
  \   |n            |
  /   |-- + 15*n - 4|
 /    \25           /
/___,                
n = 1
$$\sum_{n=1}^{\infty} \left(\left(\frac{n^{2}}{25} + 15 n\right) - 4\right)$$ 
Sum(n^2/25 + 15*n - 4, (n, 1, oo))
The radius of convergence of the power series
Given number:
$$\left(\frac{n^{2}}{25} + 15 n\right) - 4$$
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
$$a_{n} = \frac{n^{2}}{25} + 15 n - 4$$
and
$$x_{0} = 0$$
,
$$d = 0$$
,
$$c = 1$$
then
$$1 = \lim_{n \to \infty}\left(\frac{\left|{\frac{n^{2}}{25} + 15 n - 4}\right|}{15 n + \frac{\left(n + 1\right)^{2}}{25} + 11}\right)$$
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 1/25n^2+15n-4

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