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1/(n^2-3n+2)
Sum of series/ 1/(n^2-3n+2)

Sum of series 1/(n^2-3n+2)


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The solution

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

False
The rate of convergence of the power series
The answer [src] 
nan
$$\text{NaN}$$ 
nan
The graph
Sum of series 1/(n^2-3n+2)

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