Mister Exam

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How to use it?
Sum of series:
1/n!
(((-1)^(n))*(16*x)^(n))/n!
cosn/n
(3×x^n)/(4n^2-9)
Integral of d{x}:
1/(4+x^2)
Limit of the function:
1/(4+x^2)
Identical expressions
one /(four +x^ two)
1 divide by (4 plus x squared )
one divide by (four plus x to the power of two)
1/(4+x2)
1/4+x2
1/(4+x²)
1/(4+x to the power of 2)
1/4+x^2
1 divide by (4+x^2)
Similar expressions
1/(4-x^2)

Sum of series/ 1/(4+x^2)

Sum of series 1/(4+x^2)

The solution

You have entered [src]

  oo        
____        
\   `       
 \      1   
  \   ------
  /        2
 /    4 + x 
/___,       
n = 1

\sum_{n=1}^{\infty} \frac{1}{x^{2} + 4}

Sum(1/(4 + x^2), (n, 1, oo))

The radius of convergence of the power series

Given number:

\frac{1}{x^{2} + 4}

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} = \frac{1}{x^{2} + 4}

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  
------
     2
4 + x

\frac{\infty}{x^{2} + 4}

oo/(4 + x^2)

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
```