How does discarding a spent rocket stage increase a missile’s range?

Discarding a spent rocket stage increases a missile’s range by reducing the vehicle's total mass as the flight progresses. By burning through its propellant and then shedding the now-useless hardware—such as empty fuel tanks, pumps, flight controls, and associated structural equipment—each successive stage has significantly less mass to accelerate. This reduction in mass allows the remaining stages to achieve higher velocities and travel farther, while also enabling the missile to carry a larger payload.12