Mister Exam

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How to use it?
Sum of series:
n^3/2^n
nx^(n+1)
21
pi^(2*n)/factorial(2*n)
Limit of the function:
21
Identical expressions
twenty-one
21
twenty minus one
Similar expressions
((n^2)^1/3)*atan(1/n^2)
2*(1/n^3+5n+6)
((-1)^(n-1)/(((n^3)+2)^(1/2)))

Sum of series/ 21

Sum of series 21

The solution

You have entered [src]

  oo    
 __     
 \ `    
  )   21
 /_,    
n = 1

\sum_{n=1}^{\infty} 21

Sum(21, (n, 1, oo))

The radius of convergence of the power series

Given number:

21

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} = 21

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

Numerical answer

The series diverges

The graph

Sum of series 21

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
```