Mister Exam

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Sum of series:
1/4^n
cos(xi+yi)
sin(nx)
(3-2i-5i^2+8i^3)
Integral of d{x}:
sin(nx)
Derivative of:
sin(nx)
Identical expressions
sin(nx)
sinus of (nx)
sinnx
Similar expressions
sin(n*x)/n^3
sin(n*x)/5^n
sin(n*x)

Sum of series/ sin(nx)

Sum of series sin(nx)

The solution

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

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

Sum(sin(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
```