calculus II
posted by SDSU on .
a ball is dropped from a height of 100 ft. Each time it hits the floor, it rebounds to 2/3 its previous height. Find the total distance traveled.

Calculate the limit of the series
100[1 + 2*(2/3) + 2*(2/3)^2 + 2*(2/3)^3+...]
= 100 + 2[1 + 2/3 + (2/3)^2+ ...]
Make use of the relation:
1 + x + x^2 + .. = 1/(1x)
(for x<1, which is the case here) 
= 100 [1 + (4/3)[1 + 2/3 + (2/3)^2+ ...]
= 100 {1 + (4/3)[1/(1  2/3)]} = ?