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Cauchy Sequences

  1. Mar 18, 2008 #1
    1. The problem statement, all variables and given/known data
    Prove that the following sequence is Cauchy:
    a_n = [a_(n-1) + a_(n-2)]/2 (i.e. the average of the last two), where
    a_0 = x
    a_1 = y

    2. Relevant equations

    3. The attempt at a solution
    I was trying to use the definition of Cauchy (i.e. |a_m - a_n| < e) by relating a_n - a_(n-1) to a_(n-1) - a_(n-2), but to no avail.
  2. jcsd
  3. Mar 19, 2008 #2
    can you use the theorem: every convergent sequence, is a cauchy sequence

    just prove the sequence converges, cite the theorem, and you're finished
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