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fourier series

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please give me the proof of fourier series

Nobody seems in a hurry to answer this so I will give as my opinion that proof is extremely difficult and declare that it is beyond me. However evidence that it "works" can be provided by scale drawing over a few of the necessary (in the case of the square wave infinite) number of harmonics added to a fundamental frequency. It's quite likely that you have done this and are looking for more depth - if so then sorry!

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