# Suppose you drop a ball from a height of 1 meter. This ball has thecurious

August 31, 2017

Question
Question 1-Suppose you drop a ball from a height of 1 meter. This ball has thecurious property that it always bounces exactly 2/3 as high as its previousbounce. What is the total vertical distance (NOT displacement) thatthe ball travels? So the ball travels a vertical distance of exactly 1meter before it hits the ground, then it travels two thirds of a meter of vertical distance on the bounce up, and two thirds of a meter of vertical distance on the way down and so on.

Question 2 is Consider the following sequence: {1,1/2,2/3,3/5,5/8,8/13 ,13/21 , · · ·} What is the pattern of this sequence? A correct description of the pattern is just as good as a formula. What is the limit of this sequence?

I know for the second question that it is a Fibonacci sequence divided by another so it would have a limit at the golden ratio but what would the sequence formula be for it? I know it says you can just describe the pattern but I feel stuck not being able to figure out a formula :p

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