Don't forget the ball travels down as well as up!
A 'supa-ball' is dropped from a height of 1 metre onto a level table. It always rises to a height equal to 0.9 of the height from which it was dropped. How far does it travel in total until it stops bouncing?
The consecutives heights which the ball attains form a geometric series with first term a=1 and common ratio 0.9. Using the formula for the sum to infinity of the series, I am left with S = a/(1-r) = 1/0.1 = 10 metres
However, the answer given is 19 metres. I don't understand how to get to this answer, is this just a typo?