Mister Exam

Lang:

Other calculators

How to use it?
Sum of series:
log(n/n-2)
1/(ln(x+2)*ln(x+2))
1/((ln(n+2))^n)
ln(n/(n+1))
Identical expressions
log(n/n- two)
logarithm of (n divide by n minus 2)
logarithm of (n divide by n minus two)
logn/n-2
log(n divide by n-2)
Similar expressions
log(n/n+2)
log(n/(n-2))

Sum of series log(n/n-2)

The solution

You have entered [src]

  oo            
 ___            
 \  `           
  \      /n    \
   )  log|- - 2|
  /      \n    /
 /__,           
n = 1

$$\sum_{n=1}^{\infty} \log{\left(-2 + \frac{n}{n} \right)}$$

Sum(log(n/n - 2), (n, 1, oo))

The radius of convergence of the power series

Given number:
$$\log{\left(-2 + \frac{n}{n} \right)}$$
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
$$a_{n} = i \pi$$
and
$$x_{0} = 0$$
,
$$d = 0$$
,
$$c = 1$$
then
$$1 = \lim_{n \to \infty} 1$$
Let's take the limit
we find

True

False

The answer [src]

oo*I

$$\infty i$$

oo*i

Numerical answer

The series diverges

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
```

Other calculators

How to use it?

Identical expressions

Similar expressions

Sum of series log(n/n-2)

The solution

Examples of finding the sum of a series