Mister Exam

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Sum of series:
3/(n*(n+2))
1/(n+1)!
cos(kx)
nx^(n+1)
Identical expressions
cos(kx)
co sinus of e of (kx)
coskx
Similar expressions
cos(k*x)
y-cos(k*x)^3
1+(2(-1)^(n+1))/(k^2-1)coskx

Sum of series/ cos(kx)

Sum of series cos(kx)

The solution

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  oo          
 __           
 \ `          
  )   cos(k*x)
 /_,          
k = 0

$$\sum_{k=0}^{\infty} \cos{\left(k x \right)}$$

Sum(cos(k*x), (k, 0, 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
```