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

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


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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

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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)

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