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cos(2n)/n^2

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  • Sum of series:
  • cos(2n)/n^2 cos(2n)/n^2
  • 3^(n-1)/7^n 3^(n-1)/7^n
  • arctg(x)
  • x^(n+1)/(n(n+1))

  • Identical expressions

  • cos(two n)/n^2
  • co sinus of e of (2n) divide by n squared
  • co sinus of e of (two n) divide by n squared
  • cos(2n)/n2
  • cos2n/n2
  • cos(2n)/n²
  • cos(2n)/n to the power of 2
  • cos2n/n^2
  • cos(2n) divide by n^2
Sum of series/ cos(2n)/n^2

Sum of series cos(2n)/n^2


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The solution

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

False
The rate of convergence of the power series
The graph
Sum of series cos(2n)/n^2

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