Results 1 to 2 of 2

Math Help - infinite sequence

  1. #1
    Newbie
    Joined
    Dec 2011
    Posts
    4

    infinite sequence

    What does the series converge to where
    [a_1]=√12
    [a_n+1]=√(12+a_n) ?

    I tried:
    L = √(12+√(12+√(12+...)))
    then L^2 = 12+√(12+√(12+...))
    then L^∞ = 12^∞ + 12^∞-1...+12
    thus L = ∞√(12^∞ + 12^∞-1...+12) but i dont think that this is right.

    Then someone on physics forum told me that a_n can be written as √(12+a_n+1) so a_n+1 converges because it is in the series itself, but what is the limit?
    Attached Thumbnails Attached Thumbnails infinite sequence-screen-shot-2011-12-06-10.38.40-pm.png  
    Last edited by CaptainBlack; December 7th 2011 at 12:04 AM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4

    Re: infinite series

    Quote Originally Posted by jaqueh View Post
    What does the series converge to where
    [a_1]=√12
    [a_n+1]=√(12+a_n) ?

    I tried:
    L = √(12+√(12+√(12+...)))
    then L^2 = 12+√(12+√(12+...))
    then L^∞ = 12^∞ + 12^∞-1...+12
    thus L = ∞√(12^∞ + 12^∞-1...+12) but i dont think that this is right.

    Then someone on physics forum told me that a_n can be written as √(12+a_n+1) so a_n+1 converges because it is in the series itself, but what is the limit?
    If this converges the limit should satisfy:

    L=\sqrt{12+L}

    squaring:

    L^2=12+L

    rearranging:

    L^2-L-12=0

    This has exactly one positive root and it is the limit you seek.

    CB
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Infinite sequence help
    Posted in the Calculus Forum
    Replies: 3
    Last Post: March 12th 2011, 03:24 PM
  2. Replies: 7
    Last Post: October 12th 2009, 11:10 AM
  3. Infinite Sequence
    Posted in the Calculus Forum
    Replies: 2
    Last Post: March 15th 2009, 11:21 PM
  4. Another infinite sequence
    Posted in the Calculus Forum
    Replies: 4
    Last Post: March 15th 2009, 11:17 PM
  5. another infinite sequence
    Posted in the Calculus Forum
    Replies: 1
    Last Post: March 8th 2009, 06:13 PM

Search Tags


/mathhelpforum @mathhelpforum