Fourier series provide a powerful way to represent complicated periodic functions as infinite sums of simple sine and cosine waves. The central idea is that any reasonably well-behaved periodic function can be decomposed into a weighted combination of oscillations with different frequencies, amplitudes, and phases. These basic waves act like building blocks: low-frequency terms capture the overall shape of the function, while higher-frequency terms refine its details. Mathematically, the coeffic
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