Results 1 to 2 of 2

Math Help - Solving for the limit of this sequence

  1. #1
    Member
    Joined
    Mar 2009
    Posts
    168

    Solving for the limit of this sequence

    a_{1}=1
    a_{n+1}=\sqrt{1+\sqrt{a_{n}}}

    So, taking the limit of both sides, call the limit A, gives us
    A=lim \sqrt{1+\sqrt{a_{n}}}= \sqrt{1+\sqrt{A}}

    Solving for A gives us
    A^2=1+\sqrt{A} or
    A^2-\sqrt{A}-1=0

    I'm assuming I did all of the above correctly. My only issue now is... how do I solve for A?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by paupsers View Post
    a_{1}=1
    a_{n+1}=\sqrt{1+\sqrt{a_{n}}}

    So, taking the limit of both sides, call the limit A, gives us
    A=lim \sqrt{1+\sqrt{a_{n}}}= \sqrt{1+\sqrt{A}}

    Solving for A gives us
    A^2=1+\sqrt{A} or
    A^2-\sqrt{A}-1=0

    I'm assuming I did all of the above correctly. My only issue now is... how do I solve for A?
    A^2 - 1 = \sqrt{A} \Rightarrow (A^2 - 1)^2 = A \Rightarrow A^4 - 2A^2 - A + 1 = 0. Solve for A.

    There are some other things you need to do as well, like showing that the sequence is bounded.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. limit of a sequence
    Posted in the Differential Geometry Forum
    Replies: 8
    Last Post: August 28th 2011, 11:26 AM
  2. Replies: 2
    Last Post: October 26th 2010, 11:23 AM
  3. Sequence and limit
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: September 28th 2010, 08:55 PM
  4. limit of a sequence?
    Posted in the Calculus Forum
    Replies: 1
    Last Post: April 15th 2010, 07:31 AM
  5. Limit of a sequence.
    Posted in the Math Topics Forum
    Replies: 0
    Last Post: October 18th 2008, 12:55 PM

Search Tags


/mathhelpforum @mathhelpforum