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

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


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The solution

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

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