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Sum of series n!/(k!(n-k!))×cos(kx)



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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))

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