Sum of series (2x-4)

The solution

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  oo           
 __            
 \ `           
  )   (2*x - 4)
 /_,           
i = 1

$$\sum_{i=1}^{\infty} \left(2 x - 4\right)$$

Sum(2*x - 4, (i, 1, oo))

The radius of convergence of the power series

Given number:
$$2 x - 4$$
It is a series of species
$$a_{i} \left(c x - x_{0}\right)^{d i}$$
- power series.
The radius of convergence of a power series can be calculated by the formula:
$$R^{d} = \frac{x_{0} + \lim_{i \to \infty} \left|{\frac{a_{i}}{a_{i + 1}}}\right|}{c}$$
In this case
$$a_{i} = 2 x - 4$$
and
$$x_{0} = 0$$
,
$$d = 0$$
,
$$c = 1$$
then
$$1 = \lim_{i \to \infty} 1$$
Let's take the limit
we find

True

False

The answer [src]

oo*(-4 + 2*x)

$$\infty \left(2 x - 4\right)$$

oo*(-4 + 2*x)

Examples of finding the sum of a series

The Sum of the Power Series
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```
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```
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Flint Hills Series
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csc(n)^2/n^3
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Basel problem
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1/n^2
```
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1/n^4
```
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Harmonic series
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1/n
```
Grandi's series
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(-1)^n
```
Alternating series
```
(-1)^(n + 1)/n
```
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(n + 2)*(-1)^(n - 1)
```
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```
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(-1)^(n - 1)*n/(6*n - 5)
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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 (2x-4)

The solution

Examples of finding the sum of a series