why do we expand any periodic function by fourier series not by any other series?

Answer 1

You can use anything you want. It's just tha using the Fourier is very convenient in radio and communications because it takes you from the time domain to the frequency domain which is where telecommunications operate. It's also useful in thermodynamics, optics and mechanics but it shines in communications.

Answer 2

Would u attempt ur Hw , or at least post it in HW help rather than engineering