Question

say you drop a ball 25 meters above the ground the ball bounces 75% of the previous height with each bounce. Find the total number of metres the ball travels between the time it is dropped and the 10th bounce

Answer 1

leave the first 25 alone, add that in at the end
goes up \(.75\times25\)and down \(.75\times 25\)for a total of \(50\times .75\)
then up and down \(50\times .75^2\) etc add
\[50\times .75+50\times .75^2+50\times 275^3+...+50\times .75^9\]