Question 1188229


let the total distance travelled by the ball before coming to rest be {{{d}}}

{{{d = 100 + 2*100*(1/3)}}}*[{{{1 + 1/3 + (1/3)^2 + (1/3)^3}}} + …….. + {{{(1/3)^(infinity)}}}] [the factor {{{2}}} is for equal distance being covered up and down after each bounce of the ball]

{{{d = 100 + 2*100*(1/3)}}}}*(sum of an infinite GP series whose 1st term is 1 and common ratio is {{{1/3}}})

{{{d = 100 + 2*100*(1/3)*(1/(1 - 1/3))}}}

{{{d = 100 + 2*100*(1/3)*(3/2) }}}

{{{d= 200m}}}