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6/(n^2-10n+24)
Sum of series/ 6/(n^2-10n+24)

Sum of series 6/(n^2-10n+24)


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The solution

You have entered [src] 
  oo                
____                
\   `               
 \          6       
  \   --------------
  /    2            
 /    n  - 10*n + 24
/___,               
n = 7
$$\sum_{n=7}^{\infty} \frac{6}{\left(n^{2} - 10 n\right) + 24}$$ 
Sum(6/(n^2 - 10*n + 24), (n, 7, oo))
The radius of convergence of the power series
Given number:
$$\frac{6}{\left(n^{2} - 10 n\right) + 24}$$
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
$$a_{n} = \frac{6}{n^{2} - 10 n + 24}$$
and
$$x_{0} = 0$$
,
$$d = 0$$
,
$$c = 1$$
then
$$1 = \lim_{n \to \infty}\left(6 \left|{\frac{- \frac{5 n}{3} + \frac{\left(n + 1\right)^{2}}{6} + \frac{7}{3}}{n^{2} - 10 n + 24}}\right|\right)$$
Let's take the limit
we find
True

False
The rate of convergence of the power series
The answer [src] 
9/2
$$\frac{9}{2}$$ 
9/2
Numerical answer [src] 
4.50000000000000000000000000000
4.50000000000000000000000000000
The graph
Sum of series 6/(n^2-10n+24)

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