Mister Exam

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Sum of series:
6/((3n-2)(3n+4))
(n-1)/2^(n+1)
1/((4n-3)(4n+1))
k^2
Derivative of:
1/x^6
Integral of d{x}:
1/x^6
Identical expressions
one /x^ six
1 divide by x to the power of 6
one divide by x to the power of six
1/x6
1/x⁶
1 divide by x^6

Sum of series/ 1/x^6

Sum of series 1/x^6

The solution

You have entered [src]

  oo     
____     
\   `    
 \     1 
  \    --
  /     6
 /     x 
/___,    
n = 10

$$\sum_{n=10}^{\infty} \frac{1}{x^{6}}$$

Sum(1/(x^6), (n, 10, oo))

The radius of convergence of the power series

Given number:
$$\frac{1}{x^{6}}$$
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
$$a_{n} = \frac{1}{x^{6}}$$
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
--
 6
x

$$\frac{\infty}{x^{6}}$$

oo/x^6

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 1/x^6

The solution

Examples of finding the sum of a series