What is result of this summation:sum(k=1, to n) sin(n*pi/k)I

[Emilijo]

What is result of this summation:

sum(k=1, to n) sin(n*pi/k)

I put it in wolfram alpha but it doesn't give me the solution.
Where is the problem?

 

[tiny-tim]

try using sinθ = Im(e^iθ)

 

[Emilijo]

try using sinθ = Im(e^iθ)

No, still doesn't calculate it.

 

[rbj]

What is result of this summation:

$$\sum_{k=1}^n \sin(n \pi / k)$$

I put it in wolfram alpha but it doesn't give me the solution.
Where is the problem?

try using sinθ = Im(e^iθ)

No, still doesn't calculate it.

first of all, are you sure it isn't

$$\sum_{k=1}^n \sin(k \pi / n)$$

instead?

second, in any case, complex numbers and variables, Euler's formula, and the sum of a geometric series are three mathematical methods that are your friends.