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Homework Help: Sequence {an} that is eventually constant.

  1. Nov 27, 2005 #1
    The Sequence {an} is eventually constant.


    A sequence {an} is eventually constant if there exists an index n*EN s.t. an = C for all n>n*.

    What am I missing?
     
  2. jcsd
  3. Nov 27, 2005 #2

    matt grime

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    We have no idea, what do you think you're missing?
     
  4. Nov 27, 2005 #3

    HallsofIvy

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    In other words, the sequence
    1, 6, 9, 8.9, -33, 51.6, -23, 7, 7, 7, 7, ....7, 7, 7....
    is "eventually constant".
     
  5. Nov 27, 2005 #4

    benorin

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    Your definition seems ok, that is I googled for it a found that if a sequence is eventually constant, then its range is a finite point set, which is consistant with your definition.
     
  6. Nov 27, 2005 #5
    What about;

    The sequence {an} is eventually increasing.

    A sequence {an} is eventually increasing if and only if there exists an index n*E N s.t. an _<_ am for all m>n _>_ n*

    Is that right?
     
  7. Nov 28, 2005 #6

    matt grime

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    I've never seen anyone need or bother to define that concept before, but if they were to then that is what i imagine it would look like
     
  8. Nov 28, 2005 #7

    HallsofIvy

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    It is generally true that any finite number of terms in a sequence can be changed or eliminated without changing the limit of the sequence. That is why "eventually" some property is important. A sequence that is "eventually constant" can be treated like a constant sequence (so its limit is that constant) and a sequence that is "eventually increasing" can be treated like an increasing sequence (so if it has an upper bound it converges).
     
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