SOLUTION: Please help me solve this problem: How far up and down will a ball travel before stopping if it is dropped from a height of 12m, and each rebound is 1/3 of the previous distance

Question 128932: Please help me solve this problem:
How far up and down will a ball travel before stopping if it is dropped from a height of 12m, and each rebound is 1/3 of the previous distance?
Thank you.
Answer by oscargut(2103) (Show Source): You can put this solution on YOUR website!
first it goes down 12mts
then it goes up 4 mts (1/3 of 12mts)
then it goes down 4 mts
then it goes up 4/3 mts
then it goes down 4/3 mts
so to find the total up and down you have to sum 12+4+4+4/3+4/3....
12+ 2(4 (1+1/3+1/9+1/27+......)) =12+8(1+1/3+1/9+1/27+....)
= 12+8(1/(1-1/3))=12+8(3/2)=24 mts
note that the serie 1+1/3+1/9+1/27+.... is a geometric serie with ratio 1/3 and the sum is 1/(1-1/3)=3/2
R:24 mts

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