 Geometric bounce sequence

For repeated vertical collisions with a fixed plate and constant coefficient of restitution $0\le \gamma <1$, each collision multiplies the upward speed by $\gamma$, so successive peak heights form the displayed geometric sequence. The initial fall plus both legs of every rebound have total distance $h_0(1+{\gamma }^2)/(1-{\gamma }^2)$. The idealized impact times accumulate in finite time when $\gamma <1$; real contact mechanics replaces the limiting sequence by rest.