Sum of series x1

The solution

You have entered [src]

  oo    
 __     
 \ `    
  )   x1
 /_,    
x = 1

$$\sum_{x=1}^{\infty} x_{1}$$

Sum(x1, (x, 1, oo))

The radius of convergence of the power series

Given number:
$$x_{1}$$
It is a series of species
$$a_{x} \left(c x - x_{0}\right)^{d x}$$
- power series.
The radius of convergence of a power series can be calculated by the formula:
$$R^{d} = \frac{x_{0} + \lim_{x \to \infty} \left|{\frac{a_{x}}{a_{x + 1}}}\right|}{c}$$
In this case
$$a_{x} = x_{1}$$
and
$$x_{0} = 0$$
,
$$d = 0$$
,
$$c = 1$$
then
$$1 = \lim_{x \to \infty} 1$$
Let's take the limit
we find

True

False

The answer [src]

oo*x1

$$\infty x_{1}$$

oo*x1

Examples of finding the sum of a series

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```
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```
1/2^(n!)
```
```
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```
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x^n/n!
```
```
k!/(n!*(n+k)!)
```
Flint Hills Series
```
csc(n)^2/n^3
```
Basel problem
```
1/n^2
```
```
1/n^4
```
```
1/n^6
```
Harmonic series
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1/n
```
Grandi's series
```
(-1)^n
```
Alternating series
```
(-1)^(n + 1)/n
```
```
(n + 2)*(-1)^(n - 1)
```
```
(3*n - 1)/(-5)^n
```
```
(-1)^(n - 1)*n/(6*n - 5)
```
Newton–Mercator series
```
(-1)^(n + 1)/n*x^n
```
Exam the series for convergence
```
(3*n - 1)/(-5)^n
```

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Sum of series x1

The solution

Examples of finding the sum of a series