Mister Exam

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Sum of series:
1/(r+1)
lnn/(n((ln^4)(n+1)))
n/9^n
log(n/n-2)
Identical expressions
one /(r+ one)
1 divide by (r plus 1)
one divide by (r plus one)
1/r+1
1 divide by (r+1)
Similar expressions
1/(r-1)

Sum of series/ 1/(r+1)

Sum of series 1/(r+1)

The solution

You have entered [src]

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

$$\sum_{r=1}^{\infty} \frac{1}{r + 1}$$

Sum(1/(r + 1), (r, 1, oo))

The radius of convergence of the power series

Given number:
$$\frac{1}{r + 1}$$
It is a series of species
$$a_{r} \left(c x - x_{0}\right)^{d r}$$
- power series.
The radius of convergence of a power series can be calculated by the formula:
$$R^{d} = \frac{x_{0} + \lim_{r \to \infty} \left|{\frac{a_{r}}{a_{r + 1}}}\right|}{c}$$
In this case
$$a_{r} = \frac{1}{r + 1}$$
and
$$x_{0} = 0$$
,
$$d = 0$$
,
$$c = 1$$
then
$$1 = \lim_{r \to \infty}\left(\frac{r + 2}{r + 1}\right)$$
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 1/(r+1)

The solution

Examples of finding the sum of a series