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sinn/n^2

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  • Sum of series:
  • sinn/n^2 sinn/n^2
  • 1/x-1(x+1)
  • 2/n^2 2/n^2
  • 1/(n*log(n)) 1/(n*log(n))

  • Identical expressions

  • sinn/n^ two
  • sinus of n divide by n squared
  • sinus of n divide by n to the power of two
  • sinn/n2
  • sinn/n²
  • sinn/n to the power of 2
  • sinn divide by n^2
Sum of series/ sinn/n^2

Sum of series sinn/n^2


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The solution

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

False
The rate of convergence of the power series
The graph
Sum of series sinn/n^2

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