Sum of series ax

The solution

You have entered [src]

  oo     
 __      
 \ `     
  )   a*x
 /_,     
a = 3

$$\sum_{a=3}^{\infty} a x$$

Sum(a*x, (a, 3, oo))

The radius of convergence of the power series

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

The Sum of the Power Series
```
x^n/n
```
```
(x-1)^n
```
Factorial
```
1/2^(n!)
```
```
n^2/n!
```
```
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
```
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 ax

The solution

Examples of finding the sum of a series