The sum of the geometric series (distance bounced) is given by 2+0.8*2+0.8^2 *2+0.8^3 *2 +...=
2(1+0.8+0.8^2+0.8^3+...)=2(1-0.8^n)/(1-0.8) = 10(1-0.8^n), where n is the nth term.
When n=1 (first bounce), distance=10(0.2)=2m.
When n gets very large 0.8^n approaches 0 and the sum=10m.