Mister Exam

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Sum of series:
(arcsin(1/n))^n
1/(n^2-3n+2)
(1-x^4)^n/(n+2)
log((n+2)/n)^((-1)^(n+1))
Derivative of:
x^3
Integral of d{x}:
x^3
Equation:
x^3
Identical expressions
x^ three
x cubed
x to the power of three
x3
x³
x to the power of 3

Sum of series/ x^3

Sum of series x^3

The solution

You have entered [src]

  oo    
 ___    
 \  `   
  \    3
  /   x 
 /__,   
x = 1

$$\sum_{x=1}^{\infty} x^{3}$$

Sum(x^3, (x, 1, oo))

The radius of convergence of the power series

Given number:
$$x^{3}$$
It is a series of species
$$a_{x} \left(c x - x_{0}\right)^{d x}$$
- power series.
The radius of convergence of a power series can be calculated by the formula:
$$R^{d} = \frac{x_{0} + \lim_{x \to \infty} \left|{\frac{a_{x}}{a_{x + 1}}}\right|}{c}$$
In this case
$$a_{x} = x^{3}$$
and
$$x_{0} = 0$$
,
$$d = 0$$
,
$$c = 1$$
then
$$1 = \lim_{x \to \infty}\left(\frac{x^{3}}{\left(x + 1\right)^{3}}\right)$$
Let's take the limit
we find

True

False

The rate of convergence of the power series

The answer [src]

oo

$$\infty$$

oo

Numerical answer

The series diverges

The graph

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

Sum of series x^3

The solution

Examples of finding the sum of a series