Mister Exam

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Sum of series:
x^n/n^2
sin(n*x)/n^3
log(1+1/n)
ln(1+1/n)
Integral of d{x}:
x/(x-1)
Graphing y =:
x/(x-1)
Derivative of:
x/(x-1)
Identical expressions
x/(x- one)
x divide by (x minus 1)
x divide by (x minus one)
x/x-1
x divide by (x-1)
Similar expressions
x/(x+1)

Sum of series/ x/(x-1)

Sum of series x/(x-1)

The solution

You have entered [src]

  oo       
 ___       
 \  `      
  \     x  
   )  -----
  /   x - 1
 /__,      
x = 2

$$\sum_{x=2}^{\infty} \frac{x}{x - 1}$$

Sum(x/(x - 1), (x, 2, oo))

The radius of convergence of the power series

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

Similar expressions

Sum of series x/(x-1)

The solution

Examples of finding the sum of a series