A ball is dropped from a height of 10 m and rebounds to 80 % of the previous height…
MATHEMATICS · Subjective · A Level · Mathematics · Sequences and series · Sequences and series
Problem
A ball is dropped from a height of 10 m and rebounds to 80\% of the previous height after every bounce. Let Dn denote the total vertical distance the ball has traveled after n complete rebounds (each rebound includes both the upward and downward segments). Find the smallest integer n for which Dn is at least 99\% of the ball’s total vertical distance over all time.