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## Homework Statement

Let [tex]\hat{u}_k[/tex] the Fourier coefficients of 2-periodic function [tex]u(t)=t[/tex] with [tex]t\in [0,2)[/tex]. Evaluate the sum of the serie:

[tex]\sum_{k=-\infty}^{\infty}\hat{u}_k e^{\pi i k t}[/tex] for [tex]t= 2[/tex]

Ok, I think there is a trick that I don't know...

[tex]\sum_{k=-\infty}^{\infty}\hat{u}_k e^{\pi i k t}[/tex] for [tex]t= 2[/tex]

becomes

[tex]\sum_{k=-\infty}^{\infty}\hat{u}_k [/tex]

What can i do now? Any help will be appreciated :)