1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Cauchy Sequences
  1. Cauchy sequence (Replies: 4)

  2. Cauchy sequence (Replies: 1)

  3. Cauchy Sequence (Replies: 10)

  4. Cauchy Sequence (Replies: 9)

  5. Cauchy sequence (Replies: 2)