Mister Exam

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How to use it?
Sum of series:
(3/4)^n
1/((2n-1)*(2n+1))
1/(n*(n+3))
(5/6)^n
Integral of d{x}:
arctgx/x
Identical expressions
arctgx/x
arctgx divide by x
Similar expressions
(x-arctgx)/x^2

Sum of series/ arctgx/x

Sum of series arctgx/x

The solution

You have entered [src]

  1          
 ___         
 \  `        
  \   acot(x)
   )  -------
  /      x   
 /__,        
n = 0

$$\sum_{n=0}^{1} \frac{\operatorname{acot}{\left(x \right)}}{x}$$

Sum(acot(x)/x, (n, 0, 1))

The answer [src]

2*acot(x)
---------
    x

$$\frac{2 \operatorname{acot}{\left(x \right)}}{x}$$

2*acot(x)/x

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
```