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Limit of (2.3, 2.33, 2.333, )

  1. Nov 2, 2011 #1
    1. The problem statement, all variables and given/known data
    Compute the limit of the following sequences (show work):
    (2.3, 2.33, 2.333, 2.3333, ...)


    3. The attempt at a solution
    Theoretically it approaches 2.333... but I don't think this is the correct answer (and I am not sure how to show it). Does the limit not exist?
     
  2. jcsd
  3. Nov 2, 2011 #2

    Mark44

    Staff: Mentor

    If the sequence happened to be (0.3, 0.33, 0.333, 0.3333, ...), what would the limit of the sequence be? The limit of your sequence is 2 plus the limit of this sequence.
     
  4. Nov 2, 2011 #3

    LCKurtz

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    Gold Member

    Remember that a repeating decimal represents a rational number. You should be able to express it as a fraction.
     
  5. Nov 2, 2011 #4
    Wow, that is so simple. Thank you!
     
  6. Nov 2, 2011 #5

    LCKurtz

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    How "simple" it is depends on how detailed the "show your work" is supposed to be.
     
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