Mister Exam

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Sum of series:
(2/5)^n
sqrt(x^n+y^n)^2-(32^(1/3*n)*x*y)^n
sin(x(2k-1))
cos(2*n)/n^2
Identical expressions
sin(x(2k- one))
sinus of (x(2k minus 1))
sinus of (x(2k minus one))
sinx2k-1
Similar expressions
sin(x(2k+1))

Sum of series/ sin(x(2k-1))

Sum of series sin(x(2k-1))

The solution

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  n                   
 __                   
 \ `                  
  )   sin(x*(2*k - 1))
 /_,                  
k = 1

$$\sum_{k=1}^{n} \sin{\left(x \left(2 k - 1\right) \right)}$$

Sum(sin(x*(2*k - 1)), (k, 1, n))

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
```