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Sum of series/ (sin(x))^2

Sum of series (sin(x))^2


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The solution

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  oo         
 ___         
 \  `        
  \      2   
  /   sin (x)
 /__,        
n = 1
$$\sum_{n=1}^{\infty} \sin^{2}{\left(x \right)}$$ 
Sum(sin(x)^2, (n, 1, oo))
The radius of convergence of the power series
Given number:
$$\sin^{2}{\left(x \right)}$$
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
$$a_{n} = \sin^{2}{\left(x \right)}$$
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] 
      2   
oo*sin (x)
$$\infty \sin^{2}{\left(x \right)}$$ 
oo*sin(x)^2

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