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

  • Identical expressions

  • y-cos(k*x)^ three
  • y minus co sinus of e of (k multiply by x) cubed
  • y minus co sinus of e of (k multiply by x) to the power of three
  • y-cos(k*x)3
  • y-cosk*x3
  • y-cos(k*x)³
  • y-cos(k*x) to the power of 3
  • y-cos(kx)^3
  • y-cos(kx)3
  • y-coskx3
  • y-coskx^3

  • Similar expressions

  • y+cos(k*x)^3
Sum of series/ y-cos(k*x)^3

Sum of series y-cos(k*x)^3


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The solution

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

False
The answer [src] 
   /       3     \
oo*\y - cos (k*x)/
$$\infty \left(y - \cos^{3}{\left(k x \right)}\right)$$ 
oo*(y - cos(k*x)^3)

    Examples of finding the sum of a series

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