Question 1152042
Ball drops {{{12m}}} in the first step.

It rebounds {{{6m}}} and drops back {{{6m}}} covering {{{12m}}} in the second step.

It rebounds {{{3m}}} and drops back {{{3m}}} covering {{{6m}}} in the third step.

This continues indefinitely.

Mathematically :

{{{S = 12 + 12 + 6 + 3}}}+...{{{infinity}}}

= {{{12 }}}+ ({{{12 + 6 + 3}}} +...{{{infinity}}})


Now ({{{12 + 6 + 3}}} +...{{{infinity}}}) is an infinite GP with {{{a = 12}}} and {{{r = 1/2}}}


=> {{{S = 12 + (12/(1 - 1/2))}}} 

=> {{{S = 12 + (12/(1/2))}}}

=> {{{S = 12 + 24)}}}

=> {{{S = 36m}}}