Mister Exam

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Sum of series:
24/(9n^2-12n-5)
n^(2/3)*arctg(1/n^2)
2/(n^2+6n+8)
tan(n*x)
Identical expressions
tan(n*x)
tangent of (n multiply by x)
tan(nx)
tannx

Sum of series/ tan(n*x)

Sum of series tan(n*x)

The solution

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  oo          
 __           
 \ `          
  )   tan(n*x)
 /_,          
n = 1

$$\sum_{n=1}^{\infty} \tan{\left(n x \right)}$$

Sum(tan(n*x), (n, 1, oo))

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
```