Results 1 to 4 of 4

Math Help - Sequence Convergence

  1. #1
    Newbie
    Joined
    Sep 2009
    Posts
    2

    Sequence Convergence

    so the sequence is

    { \sqrt2, \sqrt(2+\sqrt2),\sqrt(2+\sqrt(2+\sqrt2), ... }

    i need to prove by induction that the sequence is monotonic and bounded.
    i can see how its monotonic, but how do i prove its bounded? and what is induction?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,705
    Thanks
    1637
    Awards
    1
    Quote Originally Posted by ixion124 View Post
    so the sequence is

    { \sqrt2, \sqrt(2+\sqrt2),\sqrt(2+\sqrt(2+\sqrt2), ... }

    i need to prove by induction that the sequence is monotonic and bounded.
    i can see how its monotonic, but how do i prove its bounded? and what is induction?
    Work with s_1=\sqrt2, n\ge2,~s_n=\sqrt{2+s_{n-1}}.
    Use induction.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Sep 2009
    Posts
    2
    thanks!
    but how would i prove it with induction?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,705
    Thanks
    1637
    Awards
    1
    Show that s_1\le s_2\le 2.

    Show that if s_N\le s_{N+1}\le 2 then s_{N+1}\le s_{N+2}\le 2.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. convergence of a sequence
    Posted in the Differential Geometry Forum
    Replies: 9
    Last Post: March 24th 2011, 03:11 PM
  2. Replies: 7
    Last Post: October 12th 2009, 10:10 AM
  3. Replies: 6
    Last Post: October 1st 2009, 09:10 AM
  4. Convergence of sequence
    Posted in the Calculus Forum
    Replies: 3
    Last Post: September 23rd 2009, 05:33 AM
  5. Replies: 6
    Last Post: October 24th 2008, 01:45 PM

Search Tags


/mathhelpforum @mathhelpforum