Mathematica: This Fourier series periodic function will generate zero, what's wrong?

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This Fourier series periodic function will generate zero, what's wrong?
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(mathematica.stackexchange.com/users/65814/kile)kile
(mathematica.stackexchange.com/users/92236/kevin-dietrich)Kevin Dietrich
(mathematica.stackexchange.com/users/57128/rmw)rmw
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