Results 1 to 4 of 4

Math Help - Recursion Problem!

  1. #1
    Newbie
    Joined
    Feb 2014
    From
    Minneapolis
    Posts
    12

    Recursion Problem!

    Let x_0 be a real number in the interval (0,1] and {x_n} be sequence for all n >= 0, defined inductively by setting x_n = sin(x_(n-1)) for all n >= 1. I have already proved that {x_n} is a strictly decreasing sequence in (0,1] and that the lim x_n asn→∞ = 0.

    We need to prove parts 2 and 3 in the attachment!
    Recursion Problem!-20140221_022505.jpg

    Thanks!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Nov 2013
    From
    California
    Posts
    2,789
    Thanks
    1149
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member
    Joined
    Dec 2012
    From
    Athens, OH, USA
    Posts
    713
    Thanks
    298

    Re: Recursion Problem!

    Hi,
    A solution to the 2nd problem is just a lengthy application of L'hopital's rule. The attachment has most of the details:

    Recursion Problem!-mhfcalc35.png
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Super Member
    Joined
    Dec 2012
    From
    Athens, OH, USA
    Posts
    713
    Thanks
    298

    Re: Recursion Problem!

    Hi again,
    A "simpler" solution than my previous post is provided by the attachment. At least the derivatives involved are easily calculated.

    Recursion Problem!-mhfcalc35a.png
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Matlab Recursion Problem
    Posted in the Math Software Forum
    Replies: 0
    Last Post: September 13th 2012, 03:51 PM
  2. problem in recursion
    Posted in the Discrete Math Forum
    Replies: 0
    Last Post: November 3rd 2009, 10:51 AM
  3. Problem with understanding recursion
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: July 25th 2009, 06:24 AM
  4. Recursion problem
    Posted in the Discrete Math Forum
    Replies: 5
    Last Post: October 21st 2008, 07:11 AM
  5. Pattern/Recursion for paint can problem
    Posted in the Algebra Forum
    Replies: 1
    Last Post: September 8th 2008, 02:45 AM

Search Tags


/mathhelpforum @mathhelpforum