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Infinite Series AGAIN!

  1. Nov 21, 2007 #1
    1. The problem statement, all variables and given/known data
    When dropped, an elastic ball bounces back up to a height three-quarters of that from wich it fell. If the ball is dropped from a height 2 m and allowed to bounce up and down indefinitely, what is the total distance it travels before coming to rest?



    2. Relevant equations

    I think I have to use Partial sums of geometric series.

    If r is not equal to 1 then


    [tex] S_n = a + ar + ar^2 + ... ar^n-1 = a(1-r^n)/1-r [/tex]



    3. The attempt at a solution

    It's really easy to understand the question, but setting it up mathematecally is other story.

    I tried to do 2 + 3/2 + 9/8 + 27/32 + 81/128 + ... + 3n/4n where a_1 = 2 and a_2 = 3/2
    but this is not leading me to an final answer.

    Trying to use the equation above saying a = 2 and r = 3/4

    I get the final answer 8 m But the answer is 14 m.

    What is the correct setup?
     
  2. jcsd
  3. Nov 21, 2007 #2

    otg

    User Avatar

    If you use only 3/2+9/8+27/32+...+3n/4n where a_1=3/2, you get half the distance, save 2m [since it bounces up AND down the same distance every time except the first drop]
    S_n=8 according to your calculations, so the new sum would be S_n-2

    Thus you get the total distance as 2+2(S_n-2) = 2+12=14
     
  4. Nov 21, 2007 #3
    duh?

    Thank you for this eye opening reply.

    Of course!
     
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