Mister Exam

Lang:

Other calculators

How to use it?
Sum of series:
1/((n+14)(n+15))
1/(n+1)!
sin(pi/2^(n-1))
k^3/
Identical expressions
twenty-seven
27
twenty minus seven
Similar expressions
(2^(n+1))/(3^(n-2)*7^n)

Sum of series/ 27

Sum of series 27

The solution

You have entered [src]

  oo    
 __     
 \ `    
  )   27
 /_,    
n = 2

\sum_{n=2}^{\infty} 27

Sum(27, (n, 2, oo))

The radius of convergence of the power series

Given number:

27

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} = 27

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 rate of convergence of the power series

The answer [src]

oo

\infty

oo

Numerical answer

The series diverges

The graph

Sum of series 27

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
```