1. Limited time only! Sign up for a free 30min personal 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 sequence

  1. Jan 27, 2014 #1
    1. The problem statement, all variables and given/known data



    [tex] x_1=1 [/tex]

    Show that:


    [tex]|x_{n+1}-x_n| \leq \frac{1}{9}|x_{n}-x_{n-1}|[/tex]

    and (2) x_n is Cauchy.

    2. Relevant equations

    3. The attempt at a solution
    I've tried different approaches (including induction) but the sequence isn't monotonically decreasing.
  2. jcsd
  3. Jan 27, 2014 #2


    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    Have you tried writing out [itex] |x_{n+1} - x_{n}| [/itex] using the definition [itex] x_j = 1/(3+x_{j-1}[/itex]?
  4. Jan 27, 2014 #3
    Got it ty.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted