Sum of series xi/2

The solution

You have entered [src]

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  \   x*i
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  /    2 
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i = 4

$$\sum_{i=4}^{\infty} \frac{i x}{2}$$

Sum((x*i)/2, (i, 4, oo))

The radius of convergence of the power series

Given number:
$$\frac{i x}{2}$$
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
$$a_{i} = \frac{i x}{2}$$
and
$$x_{0} = 0$$
,
$$d = 0$$
,
$$c = 1$$
then
$$1 = \lim_{i \to \infty}\left(\frac{i}{i + 1}\right)$$
Let's take the limit
we find

True

False

The answer [src]

oo*x

$$\infty x$$

oo*x

Examples of finding the sum of a series

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```
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```
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csc(n)^2/n^3
```
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
```
(-1)^n
```
Alternating series
```
(-1)^(n + 1)/n
```
```
(n + 2)*(-1)^(n - 1)
```
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```
```
(-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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Identical expressions

Sum of series xi/2

The solution

Examples of finding the sum of a series