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Prove,( Sequence )

  1. Apr 3, 2009 #1
    1. The problem statement, all variables and given/known data

    I have no idea
    I wish If someone can help me with proving that the limit of nth term of a seq. an = to the limit of an+1

    2. Relevant equations

    we might use that an is greater of smaller than the other term wich is an+1

    3. The attempt at a solution
    we might suppose any sequn. ??
     
  2. jcsd
  3. Apr 3, 2009 #2

    CompuChip

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    Science Advisor
    Homework Helper

    You could use the definition of limit.

    [tex]\lim_{n \to \infty} a_n = L[/tex]
    iff for any [itex]\epsilon > 0[/itex] there exists an [itex]N = N_\epsilon[/itex] such that [itex]|a_n - L| < \epsilon[/itex] whenever n > N.

    Now suppose that
    [tex]\lim_{n \to \infty} a_n = L[/tex]
    and let [itex]\epsilon > 0[/itex].
    Can you now prove that
    [tex]\lim_{n \to \infty} a_{n + 1} = L[/tex]
    ?
     
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