What impedance does a 1/8-wavelength transmission line present to an RF generator when the line is open at the far end?

Just like a shorted stub, an open transmission line that is shorter than a quarter-wavelength (like 1/8-wavelength) will present a pure reactance to the generator. When starting from an open circuit (infinite impedance) and moving toward the generator, the electrical properties of the line cause it to store electrical energy, making it act like a capacitor. Thus, it presents a capacitive reactance to the RF generator. Remembering the standard behavior of short stubs is key: open stubs shorter than 1/4-wavelength are capacitive, while shorted stubs of the same length are inductive.