Mister Exam

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Sum of series:
1/(3n-2)*(3n+1)
24/(9n^2-12n-5)
ln(1-1/n^2)
cos*π*n
Identical expressions
six /(seven *n^ one)
6 divide by (7 multiply by n to the power of 1)
six divide by (seven multiply by n to the power of one)
6/(7*n1)
6/7*n1
6/(7n^1)
6/(7n1)
6/7n1
6/7n^1
6 divide by (7*n^1)

Sum of series/ 6/(7*n^1)

Sum of series 6/(7*n^1)

The solution

You have entered [src]

  oo      
____      
\   `     
 \     6  
  \   ----
  /      1
 /    7*n 
/___,     
n = 1

$$\sum_{n=1}^{\infty} \frac{6}{7 n^{1}}$$

Sum(6/((7*n^1)), (n, 1, oo))

The radius of convergence of the power series

Given number:
$$\frac{6}{7 n^{1}}$$
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
$$a_{n} = \frac{6}{7 n}$$
and
$$x_{0} = 0$$
,
$$d = 0$$
,
$$c = 1$$
then
$$1 = \lim_{n \to \infty}\left(\frac{6 \left(\frac{7 n}{6} + \frac{7}{6}\right)}{7 n}\right)$$
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 6/(7*n^1)

The solution

Examples of finding the sum of a series