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

  • How to use it?

  • Sum of series:
  • x^n/2^n
  • 1/n^3 1/n^3
  • 1/((3n-2)*(3n+1)) 1/((3n-2)*(3n+1))
  • cos2n cos2n

  • Identical expressions

  • cos(n)/(n^(two / three)+ one)
  • co sinus of e of (n) divide by (n to the power of (2 divide by 3) plus 1)
  • co sinus of e of (n) divide by (n to the power of (two divide by three) plus one)
  • cos(n)/(n(2/3)+1)
  • cosn/n2/3+1
  • cosn/n^2/3+1
  • cos(n) divide by (n^(2 divide by 3)+1)

  • Similar expressions

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

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


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The solution

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

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