The time it takes for the ball to fall from a height is given by

$\mathrm{t}=\sqrt{\frac{2\mathrm{H}}{\mathrm{g}}}$

The height up to which the ball bounces after the ${\mathrm{n}}^{\mathrm{th}}$ collision from the floor is

${\mathrm{H}}_{\mathrm{n}}={\mathrm{e}}^{2\mathrm{n}}\mathrm{H}$

$\mathrm{t}=\sqrt{\frac{2\mathrm{H}}{\mathrm{g}}}+2\sqrt{\frac{2{\mathrm{H}}_1}{\mathrm{g}}}+2\sqrt{\frac{2{\mathrm{H}}_2}{\mathrm{g}}}+\dots \infty$
$\mathrm{t}=\sqrt{\frac{2\mathrm{H}}{\mathrm{g}}}\left(1+2\mathrm{e}+2{\mathrm{e}}^2+\mathrm{ }\dots \dots ..\mathrm{\infty }\right)$
$\mathrm{t}=$$\sqrt{\frac{2\mathrm{H}}{\mathrm{g}}}\left(\frac{1+\mathrm{e}}{1-\mathrm{e}}\right)$