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(3n^2+2)/(2n^2-1)

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  • Sum of series:
  • 30 30
  • (3n^2+2)/(2n^2-1) (3n^2+2)/(2n^2-1)
  • 1/n^6 1/n^6
  • ln((n+2)/n) ln((n+2)/n)

  • Identical expressions

  • (3n^ two + two)/(two n^2- one)
  • (3n squared plus 2) divide by (2n squared minus 1)
  • (3n to the power of two plus two) divide by (two n squared minus one)
  • (3n2+2)/(2n2-1)
  • 3n2+2/2n2-1
  • (3n²+2)/(2n²-1)
  • (3n to the power of 2+2)/(2n to the power of 2-1)
  • 3n^2+2/2n^2-1
  • (3n^2+2) divide by (2n^2-1)

  • Similar expressions

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

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


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The solution

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

False
The rate of convergence of the power series
Numerical answer
The series diverges
The graph
Sum of series (3n^2+2)/(2n^2-1)

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