Why Does Adding Harmonics Not Change the Period of the Fundamental Wave?

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johnj7
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after doing several problems, i keep seeing that when you add the waveform of the fundamental with its higher harmonics, the period of the summed wave is equal to the period of the fundamental wave.

Could someone explain conceptually why this happens?

that would be much appreciated!
 
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Well, if the fundamental has period T, consider a harmonic with period T/N.

You can think of the harmonic also having period 2T/N, 3T/N, etc.