Mister Exam

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Sum of series:
(1-x^4)^n/(n+2)
a^n*cos(a)+b^n*sin(n*b)
factorial(2*n+1)/factorial(3*n-1)
factorial(6*n)/4^n
Identical expressions
- one /(x(lnx))
minus 1 divide by (x(lnx))
minus one divide by (x(lnx))
-1/xlnx
-1 divide by (x(lnx))
Similar expressions
1/(x(lnx))

Sum of series -1/(x(lnx))

The solution

You have entered [src]

  oo          
 ___          
 \  `         
  \     -1    
   )  --------
  /   x*log(x)
 /__,         
n = 1

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

Sum(-1/(x*log(x)), (n, 1, oo))

The radius of convergence of the power series

Given number:
$$- \frac{1}{x \log{\left(x \right)}}$$
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
$$a_{n} = - \frac{1}{x \log{\left(x \right)}}$$
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   
--------
x*log(x)

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

-oo/(x*log(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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How to use it?

Identical expressions

Similar expressions

Sum of series -1/(x(lnx))

The solution

Examples of finding the sum of a series