Sum of series sen^n60°

The solution

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  oo            
____            
\   `           
 \       n60    
  \   sin   (pi)
  /   ----------
 /       360    
/___,           
n = 1

$$\sum_{n=1}^{\infty} \frac{\sin^{n_{60}}{\left(\pi \right)}}{360}$$

Sum(sin(pi)^n60/360, (n, 1, oo))

The radius of convergence of the power series

Given number:
$$\frac{\sin^{n_{60}}{\left(\pi \right)}}{360}$$
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
$$a_{n} = \frac{0^{n_{60}}}{360}$$
and
$$x_{0} = 0$$
,
$$d = 0$$
,
$$c = 1$$
then
$$1 = \lim_{n \to \infty} \text{NaN}$$
Let's take the limit
we find

False

False

The answer [src]

    n60
oo*0

$$\infty 0^{n_{60}}$$

oo*0^n60

Examples of finding the sum of a series

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1/n^2
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1/n
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Grandi's series
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```
Alternating series
```
(-1)^(n + 1)/n
```
```
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```
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Newton–Mercator series
```
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```
Exam the series for convergence
```
(3*n - 1)/(-5)^n
```

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Identical expressions

Sum of series sen^n60°

The solution

Examples of finding the sum of a series