I am attempting to read through The Art of Electronics.In the early sections of The Art of Electronics the authors asks to prove the series and parallel equations. I am unsure where to start. I know KVL and KCL, and I know ohms law. I have a suspicion I need to use the fact voltage in and out must be equal in a circuit in order to prove these equations, but after writing them down I am hopelessly lost trying to connect them.
Aside from empirically proving these equations on a breadboard, how can I rigorously prove them mathematically like the author asks for?