Mister Exam

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Sum of series:
1/(n(n+2))
sin(3n)/(7n)^(1/5)
arctg1/(2n^2)
(3*n-1)/factorial(n)
Derivative of:
(x-6)^2
Identical expressions
(x- six)^ two
(x minus 6) squared
(x minus six) to the power of two
(x-6)2
x-62
(x-6)²
(x-6) to the power of 2
x-6^2
Similar expressions
(x+6)^2

Sum of series/ (x-6)^2

Sum of series (x-6)^2

The solution

You have entered [src]

  oo           
 ___           
 \  `          
  \           2
  /    (x - 6) 
 /__,          
x = 11

$$\sum_{x=11}^{\infty} \left(x - 6\right)^{2}$$

Sum((x - 6)^2, (x, 11, oo))

The radius of convergence of the power series

Given number:
$$\left(x - 6\right)^{2}$$
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
$$a_{x} = \left(x - 6\right)^{2}$$
and
$$x_{0} = 0$$
,
$$d = 0$$
,
$$c = 1$$
then
$$1 = \lim_{x \to \infty}\left(\left(x - 6\right)^{2} \left|{\frac{1}{\left(x - 5\right)^{2}}}\right|\right)$$
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

Similar expressions

Sum of series (x-6)^2

The solution

Examples of finding the sum of a series