Proof of using Fourier coefficients for root mean square calculations on periodic signals

The purpose of this work is to academically prove using Fourier coefficients of periodic signals for root mean square (RMS) calculations. In the detail, properties of Fourier series are brought to calculate RMS values of periodic signals obviously. Results from this work can confirm that this method is more convenient, efficient and simple for RMS calculations than Calculus integration technique (if Fourier coefficients are given) and can be cited for further researches.