Mister Exam

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Sum of series:
(4x)^(2n)
sin(kx/n)*x/n
2k-1
k/2^k
Identical expressions
sin(kx/n)*x/n
sinus of (kx divide by n) multiply by x divide by n
sin(kx/n)x/n
sinkx/nx/n
sin(kx divide by n)*x divide by n

Sum of series sin(kx/n)*x/n

The solution

You have entered [src]

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

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

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

The answer [src]

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

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

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

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How to use it?

Identical expressions

Sum of series sin(kx/n)*x/n

The solution

Examples of finding the sum of a series