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2/n^2

Sum of series 2/n^2



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The solution

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

False
The rate of convergence of the power series
The answer [src]
  2
pi 
---
 3 
$$\frac{\pi^{2}}{3}$$
pi^2/3
Numerical answer [src]
3.28986813369645287294483033329
3.28986813369645287294483033329
The graph
Sum of series 2/n^2

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