Question

a 'supa-ball' is dropped from a height of 1m 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? (GP infinity)

Answer 1

we have a bounce up and down
but, it is dropped from a height so the initial one doesn't count
we do

2(sum of all)-initial
infinite sum
$S_{\infty} = \frac{a_1}{1-r}$
a1=1
r=0.9

$S_{\infty} = \frac{1}{1-0.9}$
sum=1/0.1
sum=10
so
2(sum)-initial=2(10)-1=20-1=19
travels 19m