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nlnn/((n^2)-3)

  • How to use it?

  • Sum of series:
  • (-1)^n/n^2 (-1)^n/n^2
  • lnn/n^2 lnn/n^2
  • sin(kx)
  • nlnn/((n^2)-3) nlnn/((n^2)-3)

  • Identical expressions

  • nlnn/((n^ two)- three)
  • nlnn divide by ((n squared ) minus 3)
  • nlnn divide by ((n to the power of two) minus three)
  • nlnn/((n2)-3)
  • nlnn/n2-3
  • nlnn/((n²)-3)
  • nlnn/((n to the power of 2)-3)
  • nlnn/n^2-3
  • nlnn divide by ((n^2)-3)

  • Similar expressions

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

Sum of series nlnn/((n^2)-3)


∑
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The solution

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

False
The rate of convergence of the power series
The answer [src] 
  oo          
____          
\   `         
 \    n*log(n)
  \   --------
  /         2 
 /    -3 + n  
/___,         
n = 2
$$\sum_{n=2}^{\infty} \frac{n \log{\left(n \right)}}{n^{2} - 3}$$ 
Sum(n*log(n)/(-3 + n^2), (n, 2, oo))
Numerical answer
The series diverges
The graph
Sum of series nlnn/((n^2)-3)

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