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Infinite series (damn mickey mouse)

  1. Sep 13, 2007 #1
    1. The problem statement, all variables and given/known data

    the repeating decimal . 27272727 . . . can be written as an infinite series. Write it as a series and tell if it diverges/converges. If it converges, find the sum.


    Mickey, also a former student, knows how to do this one. Mickey knows enough math to write it as .27 + .0027 + .000027 . . .

    It's now an infinite series. Mickey spots the common ratio of the series as .0027/.27 = .01. Therefore, it converges!! He use the formula and presto:
    S = .27/(1 - .01) = .27/.99 = 27/99 = 3/11
    (remarkable achievement considering he's a mouse!)



    3. The attempt at a solution

    why did mickey wrote .0027 after .27?? why not .027??
     
  2. jcsd
  3. Sep 13, 2007 #2
    because .27 + .0027 + .000027 = .272727
    .27 + .027 = .297 -> .297 +.0027 = .2997 etc
     
  4. Sep 13, 2007 #3
    ahhh..haven't thought of it...thanks
     
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