Mister Exam

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Sum of series:
1
1/(n+1)!
factorial(n+2)/n^n
cos(2*n)/2^n
Identical expressions
one /n*(n+ five)
1 divide by n multiply by (n plus 5)
one divide by n multiply by (n plus five)
1/n(n+5)
1/nn+5
1 divide by n*(n+5)
Similar expressions
1/(n)*(n+5)
1/n(n+5)
1/(n*(n+5))
1/n*(n-5)
1/((n)*(n+5))

Sum of series/ 1/n*(n+5)

Sum of series 1/n*(n+5)

The solution

You have entered [src]

  oo       
 ___       
 \  `      
  \   n + 5
   )  -----
  /     n  
 /__,      
n = 1

$$\sum_{n=1}^{\infty} \frac{n + 5}{n}$$

Sum((n + 5)/n, (n, 1, oo))

The radius of convergence of the power series

Given number:
$$\frac{n + 5}{n}$$
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
$$a_{n} = \frac{n + 5}{n}$$
and
$$x_{0} = 0$$
,
$$d = 0$$
,
$$c = 1$$
then
$$1 = \lim_{n \to \infty}\left(\frac{\left(n + 1\right) \left(n + 5\right)}{n \left(n + 6\right)}\right)$$
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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Identical expressions

Similar expressions

Sum of series 1/n*(n+5)

The solution

Examples of finding the sum of a series