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

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Discussion Overview

The discussion revolves around the summation of the function sin(n*pi/k) as k ranges from 1 to n. Participants explore methods to evaluate this summation, including potential issues with computational tools like Wolfram Alpha and alternative mathematical approaches.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested, Mathematical reasoning

Main Points Raised

  • One participant questions the result of the summation sum(k=1, to n) sin(n*pi/k) and notes that Wolfram Alpha does not provide a solution.
  • Another participant suggests using the identity sinθ = Im(eiθ) as a potential method for evaluation.
  • A later reply indicates that the suggested method did not yield a calculation result.
  • There is a proposal that the original summation might actually be sum(k=1, to n) sin(k*pi/n) instead, raising a question about the formulation of the problem.
  • Additionally, participants mention that complex numbers, Euler's formula, and the sum of a geometric series could be useful mathematical tools in this context.

Areas of Agreement / Disagreement

Participants express uncertainty regarding the correct formulation of the summation and whether the proposed methods will lead to a solution. Multiple competing views on the approach to take remain unresolved.

Contextual Notes

There are limitations regarding the assumptions made about the summation's formulation, as well as the dependence on computational tools that may not provide the expected results.

Emilijo
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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?
 
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try using sinθ = Im(eiθ) :wink:
 


tiny-tim said:
try using sinθ = Im(eiθ) :wink:

No, still doesn't calculate it.
 


Emilijo said:
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?

tiny-tim said:
try using sinθ = Im(eiθ) :wink:

Emilijo said:
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.
 

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