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Arithmetic and Geometric Series (tortoise and the hare)

  1. Mar 15, 2013 #1
    1. The problem statement, all variables and given/known data
    The question is attachedk

    2. Relevant equations
    Sn = n/2[2a+(n-1)d]
    Sn = (a x (1-r^n))/1-r

    3. The attempt at a solution
    I already found the general formulas:
    Sn = n/2(40)
    Sn = (1000 x [1-0.5^n])/0.5

    And I know that there tortoise will finish the race in 100 minutes. But I don't think the hare ever finishes the race? This is the work I did so far trying to solve for the hare:
    2000 = (1000(1-0.5^n))/0.5
    1000 = 1000(1-0.5^n)
    1 = 1-0.5^n
    2 = 0.5^n
    But 0.5 the the power of anything can never equal 2?

    Thank you!
  2. jcsd
  3. Mar 15, 2013 #2

    Attached Files:

    • math.png
      File size:
      16.4 KB
  4. Mar 15, 2013 #3
    Correction* 0 = 0.5^n
    Is that the solution? The hare can never finish the race because no matter what value n is, it can never equal 0?
  5. Mar 15, 2013 #4
    Correction: it will eventually finish, but takes an infinite amount of time
  6. Mar 15, 2013 #5


    Staff: Mentor

    Isn't that a contradiction of terms?
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