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4/(n^2-12n+35)
Sum of series/ 4/(n^2-12n+35)

Sum of series 4/(n^2-12n+35)


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The solution

You have entered [src] 
  oo                
____                
\   `               
 \          4       
  \   --------------
  /    2            
 /    n  - 12*n + 35
/___,               
n = 8
$$\sum_{n=8}^{\infty} \frac{4}{\left(n^{2} - 12 n\right) + 35}$$ 
Sum(4/(n^2 - 12*n + 35), (n, 8, oo))
The radius of convergence of the power series
Given number:
$$\frac{4}{\left(n^{2} - 12 n\right) + 35}$$
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
$$a_{n} = \frac{4}{n^{2} - 12 n + 35}$$
and
$$x_{0} = 0$$
,
$$d = 0$$
,
$$c = 1$$
then
$$1 = \lim_{n \to \infty}\left(4 \left|{\frac{- 3 n + \frac{\left(n + 1\right)^{2}}{4} + \frac{23}{4}}{n^{2} - 12 n + 35}}\right|\right)$$
Let's take the limit
we find
True

False
The rate of convergence of the power series
The answer [src] 
3
$$3$$ 
3
Numerical answer [src] 
3.00000000000000000000000000000
3.00000000000000000000000000000
The graph
Sum of series 4/(n^2-12n+35)

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