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cos(3*pi*n)/(n^3+2)

  • How to use it?

  • Sum of series:
  • x^n/n
  • (n+1)^2/2^(n-1) (n+1)^2/2^(n-1)
  • 1/n^6 1/n^6
  • 1/n^n 1/n^n

  • Identical expressions

  • cos(three *pi*n)/(n^ three + two)
  • co sinus of e of (3 multiply by Pi multiply by n) divide by (n cubed plus 2)
  • co sinus of e of (three multiply by Pi multiply by n) divide by (n to the power of three plus two)
  • cos(3*pi*n)/(n3+2)
  • cos3*pi*n/n3+2
  • cos(3*pi*n)/(n³+2)
  • cos(3*pi*n)/(n to the power of 3+2)
  • cos(3pin)/(n^3+2)
  • cos(3pin)/(n3+2)
  • cos3pin/n3+2
  • cos3pin/n^3+2
  • cos(3*pi*n) divide by (n^3+2)

  • Similar expressions

  • cos(3*pi*n)/(n^3-2)
Sum of series/ cos(3*pi*n)/(n^3+2)

Sum of series cos(3*pi*n)/(n^3+2)


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The solution

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

False
The rate of convergence of the power series
The answer [src] 
  oo             
____             
\   `            
 \    cos(3*pi*n)
  \   -----------
  /           3  
 /       2 + n   
/___,            
n = 1
$$\sum_{n=1}^{\infty} \frac{\cos{\left(3 \pi n \right)}}{n^{3} + 2}$$ 
Sum(cos(3*pi*n)/(2 + n^3), (n, 1, oo))
The graph
Sum of series cos(3*pi*n)/(n^3+2)

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