Mister Exam

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Sum of series:
((2*n+4)/(5*n+7))^n*x^n
x^n/(1+x^n)
(n-2^(3*n))/(n+1)^(1/3)
(-1)^(2n+1)*x^(2n+1)/(2n+1)!
Identical expressions
n!/(k!(n-k!))×cos(kx)
n! divide by (k!(n minus k!))× co sinus of e of (kx)
n!/k!n-k!×coskx
n! divide by (k!(n-k!))×cos(kx)
Similar expressions
n!/(k!(n+k!))×cos(kx)

Sum of series n!/(k!(n-k!))×cos(kx)

The solution

You have entered [src]

  n                       
 ___                      
 \  `                     
  \        n!             
   )  -----------*cos(k*x)
  /   k!*(n - k!)         
 /__,                     
k = 0

$$\sum_{k=0}^{n} \frac{n!}{\left(n - k!\right) k!} \cos{\left(k x \right)}$$

Sum((factorial(n)/((factorial(k)*(n - factorial(k)))))*cos(k*x), (k, 0, n))

The answer [src]

  n              
 ___             
 \  `            
  \   n!*cos(k*x)
   )  -----------
  /   (n - k!)*k!
 /__,            
k = 0

$$\sum_{k=0}^{n} \frac{\cos{\left(k x \right)} n!}{\left(n - k!\right) k!}$$

Sum(factorial(n)*cos(k*x)/((n - factorial(k))*factorial(k)), (k, 0, 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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Identical expressions

Similar expressions

Sum of series n!/(k!(n-k!))×cos(kx)

The solution

Examples of finding the sum of a series