Mister Exam

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Sum of series:
tg^(2)*(6/(2n)^(1/3))*(x-24)^n
1/(2*n-1)*(2*n+1)
cos(kx)
((-1)^(n-1))*(5^n+2)*x^n
Identical expressions
(four *ln(x))/(x^ three)
(4 multiply by ln(x)) divide by (x cubed )
(four multiply by ln(x)) divide by (x to the power of three)
(4*ln(x))/(x3)
4*lnx/x3
(4*ln(x))/(x³)
(4*ln(x))/(x to the power of 3)
(4ln(x))/(x^3)
(4ln(x))/(x3)
4lnx/x3
4lnx/x^3
(4*ln(x)) divide by (x^3)

Sum of series (4*ln(x))/(x^3)

The solution

You have entered [src]

  oo          
____          
\   `         
 \    4*log(x)
  \   --------
  /       3   
 /       x    
/___,         
n = 1

$$\sum_{n=1}^{\infty} \frac{4 \log{\left(x \right)}}{x^{3}}$$

Sum((4*log(x))/x^3, (n, 1, oo))

The radius of convergence of the power series

Given number:
$$\frac{4 \log{\left(x \right)}}{x^{3}}$$
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
$$a_{n} = \frac{4 \log{\left(x \right)}}{x^{3}}$$
and
$$x_{0} = 0$$
,
$$d = 0$$
,
$$c = 1$$
then
$$1 = \lim_{n \to \infty} 1$$
Let's take the limit
we find

True

False

The answer [src]

oo*log(x)
---------
     3   
    x

$$\frac{\infty \log{\left(x \right)}}{x^{3}}$$

oo*log(x)/x^3

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
```

Other calculators

How to use it?

Identical expressions

Sum of series (4*ln(x))/(x^3)

The solution

Examples of finding the sum of a series