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## Homework Statement

Calculate the exact value of the sum from minus infinity to infinity of C

_{k}.

## Homework Equations

C

_{k}= [itex]\frac{672}{κ^{2}π^{2}}[/itex]([itex]e^{-iκ\frac{π}{2}}[/itex][itex]-[/itex][itex]e^{-iκπ}[/itex])[itex]-[/itex]2744([itex]\frac{e^{-iκ\frac{π}{14}}}{iκπ}[/itex][itex]+[/itex][itex]\frac{e^{iκ\frac{π}{14}}}{κ^{2}π^{2}}[/itex][itex]-[/itex][itex]\frac{14e^{-iκ\frac{π}{14}}}{iκ^{3}π^{3}}[/itex][itex]+[/itex][itex]\frac{14e^{ik\frac{π}{14}}}{iκ^{3}π^{3}}[/itex])[itex]+[/itex][itex]\frac{392}{κ^{2}π^{2}}[/itex]([itex]e^{iκ\frac{π}{14}}[/itex][itex]-[/itex][itex]e^{iκ\frac{π}{2}}[/itex][itex]-[/itex][itex]e^{-iκ\frac{π}{14}}[/itex][itex]+[/itex][itex]e^{-iκ\frac{π}{2}}[/itex])

## The Attempt at a Solution

I'm not good with sums, I really have no idea how to get started.

(it's somewhat urgent, I'm supposed to solve it until tomorrow)

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