Mister Exam

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Sum of series:
sin(kx/n)
1/(n((lnn)^2))
(2/9)^n
n^2/2^n
Identical expressions
sin(kx/n)
sinus of (kx divide by n)
sinkx/n
sin(kx divide by n)

Sum of series/ sin(kx/n)

Sum of series sin(kx/n)

The solution

You have entered [src]

  n           
 ___          
 \  `         
  \      /k*x\
   )  sin|---|
  /      \ n /
 /__,         
k = 1

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

Sum(sin((k*x)/n), (k, 1, n))

The answer [src]

  n           
 ___          
 \  `         
  \      /k*x\
   )  sin|---|
  /      \ n /
 /__,         
k = 1

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

Sum(sin(k*x/n), (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
```