Particle falls from height h then formula for height covered by it in nth rebound is given by

$h_n = h e^{2n}$

where e = coefficient of restitution, n = No. of rebound

Total distance travelled by particle before rebounding has stopped

$H = h + 2h_1 + 2h_2 + 2h_3 + 2h_n + ........$

$=h + 2he^{2} + 2he^{4} + 2he^{6} + 2he^{8} + ........$

$= h + 2h \left( e^{2} + e^{4} + e^{6} + e^{8} + ...... \right)$

$= h + 2h \left[\frac{e^{2}}{1 - e^{2}}\right] = h \left[1 + \frac{2e^{2}}{1 - e^{2}}\right] = h \left(\frac{1 + e^{2}}{1 - e^{2}}\right)$