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  • Sum of series:
  • ln(1-(1/n^2)) ln(1-(1/n^2))
  • yi
  • cosnx/(n/(1/3))
  • e^x^2

  • Identical expressions

  • cosnx/(n/(one / three))
  • co sinus of e of nx divide by (n divide by (1 divide by 3))
  • co sinus of e of nx divide by (n divide by (one divide by three))
  • cosnx/n/1/3
  • cosnx divide by (n divide by (1 divide by 3))

  • Similar expressions

  • cosnx/n/(1/3)
Sum of series/ cosnx/(n/(1/3))

Sum of series cosnx/(n/(1/3))


∑
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The solution

You have entered [src] 
  oo          
____          
\   `         
 \    cos(n*x)
  \   --------
   )   / n \  
  /    |---|  
 /     \1/3/  
/___,         
n = 1
oo ____ \ ` \ cos(n*x) \ -------- ) / n \ / |---| / \1/3/ /___, n = 1 
Sum(cos(n*x)/((n/(1/3))), (n, 1, oo))
The radius of convergence of the power series
Given number:
cos(n*x)
--------
 / n \  
 |---|  
 \1/3/

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
$$a_{n} = \frac{\cos{\left(n x \right)}}{3 n}$$
and
$$x_{0} = 0$$
,
$$d = 0$$
,
$$c = 1$$
then
$$1 = \lim_{n \to \infty}\left(\frac{\left(n + 1\right) \left|{\frac{\cos{\left(n x \right)}}{\cos{\left(x \left(n + 1\right) \right)}}}\right|}{n}\right)$$
Let's take the limit
we find
True

False
The answer [src] 
  oo          
 ___          
 \  `         
  \   cos(n*x)
   )  --------
  /     3*n   
 /__,         
n = 1
$$\sum_{n=1}^{\infty} \frac{\cos{\left(n x \right)}}{3 n}$$ 
Sum(cos(n*x)/(3*n), (n, 1, oo))

    Examples of finding the sum of a series

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