SOLUTION: A ball returns two-thirds of its preceding height on each bounce. It the ball is dropped from a height of 6 m, what is the total distance travelled by the ball before coming to re

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Question 1086782: A ball returns two-thirds of its preceding height on each bounce. It the ball is dropped from a height of 6 m, what is the total distance travelled by the ball before coming to rest?
Answer by math_helper(2461) About Me  (Show Source):
You can put this solution on YOUR website!
On the initial drop it falls 6m
It bounces up to 4m (=(2/3)*6)
It then falls 4m to the ground
It bounces up to (2/3)(4) = +%282%2F3%29%5E2%2A6+
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Adding all this up, with D=distance travelled:
+D+=+6+%2B+2+%2A+sum%28+%282%2F3%29%5En%2C++n=1%2C+infinity+%29%2A6+
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+sum%28+a%5En%2C+n=1%2C+infinity+%29+=+a+%2F+%281-a%29+ when |a| < 1
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+D+=+6+%2B+12+%2A+%28%282%2F3%29+%2F+%281-%282%2F3%29%29+%29++
+D+=+6+%2B+12+%2A+%282%29+
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Ans: +D+=+highlight%2830m%29+