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  • Sum of series:
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  • Identical expressions

  • cosnx/(n^ two + one)
  • co sinus of e of nx divide by (n squared plus 1)
  • co sinus of e of nx divide by (n to the power of two plus one)
  • cosnx/(n2+1)
  • cosnx/n2+1
  • cosnx/(n²+1)
  • cosnx/(n to the power of 2+1)
  • cosnx/n^2+1
  • cosnx divide by (n^2+1)

  • Similar expressions

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

Sum of series cosnx/(n^2+1)


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The solution

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

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