Mister Exam

Lang:

Other calculators

How to use it?
Sum of series:
1/(n*ln(n))
sin((n^2+3)/(n^3+2))^2
ln(1/n+2)
log((k+1)/(k+2))
Identical expressions
log((k+ one)/(k+ two))
logarithm of ((k plus 1) divide by (k plus 2))
logarithm of ((k plus one) divide by (k plus two))
logk+1/k+2
log((k+1) divide by (k+2))
Similar expressions
log((k-1)/(k+2))
log((k+1)/(k-2))

Sum of series/ log((k+1)/(k+2))

Sum of series log((k+1)/(k+2))

The solution

You have entered [src]

  oo            
 ___            
 \  `           
  \      /k + 1\
   )  log|-----|
  /      \k + 2/
 /__,           
k = 4

$$\sum_{k=4}^{\infty} \log{\left(\frac{k + 1}{k + 2} \right)}$$

Sum(log((k + 1)/(k + 2)), (k, 4, oo))

The radius of convergence of the power series

Given number:
$$\log{\left(\frac{k + 1}{k + 2} \right)}$$
It is a series of species
$$a_{k} \left(c x - x_{0}\right)^{d k}$$
- power series.
The radius of convergence of a power series can be calculated by the formula:
$$R^{d} = \frac{x_{0} + \lim_{k \to \infty} \left|{\frac{a_{k}}{a_{k + 1}}}\right|}{c}$$
In this case
$$a_{k} = \log{\left(\frac{k + 1}{k + 2} \right)}$$
and
$$x_{0} = 0$$
,
$$d = 0$$
,
$$c = 1$$
then
$$1 = \lim_{k \to \infty}\left(\frac{\log{\left(\frac{k + 1}{k + 2} \right)}}{\log{\left(\frac{k + 2}{k + 3} \right)}}\right)$$
Let's take the limit
we find

True

False

The rate of convergence of the power series

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
```

Other calculators

How to use it?

Identical expressions

Similar expressions

Sum of series log((k+1)/(k+2))

The solution

Examples of finding the sum of a series