Results 1 to 4 of 4

Math Help - infinite sequences

  1. #1
    Newbie
    Joined
    Dec 2008
    From
    USA
    Posts
    7

    Exclamation infinite sequences

    heyy everyone.
    I was having some trouble doing an assignment for math so i hope u guys can help me.
    I have to find a formula for an+1 in terms of an for this infinite sequence:

    a1 = square root of 1 + sqaure root of 1
    a2 = square root of 1 + square root of 1 + square root of 1
    a3 = squareroot of 1 + squareroot of 1 + squareroot of 1 + squareroot of 1
    ....etc (its infinite)

    help plzz!
    thx
    =]
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,914
    Thanks
    779
    Helo, 'kaleyy =]!

    I assume those are "nested" square roots.
    Otherwise, it makes no sense.


    I have to find a formula for a_{n+1} in terms of a_n for this infinite sequence:

    a_1\:=\:\sqrt{1 + \sqrt{1}}

    a_2 \:=\:\sqrt{1 + \underbrace{\sqrt{1 + \sqrt{1}}}_{\text{This is }a_1} }

    a_3 \:=\:\sqrt{1 + \underbrace{\sqrt{1 + \sqrt{1 + \sqrt{1}}}}_{\text{This is }a_2}}\quad\hdots etc.

    . . a_{n+1} \;=\;\sqrt{1 + a_n}

    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Dec 2008
    From
    USA
    Posts
    7
    ohhh that makes so much sense.
    lol i looked at the all the square roots and i panicked.
    =D
    thx soo much.
    btw they were ""nested"" square roots.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Newbie
    Joined
    Dec 2008
    From
    USA
    Posts
    7
    ok so if i had to do this same problem but i had to use 2 instead of 1 my a(n+1) wld be:
    squareroot(2 + an)

    right?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. infinite sequences and series
    Posted in the Calculus Forum
    Replies: 4
    Last Post: October 26th 2009, 07:04 PM
  2. infinite sequences
    Posted in the Calculus Forum
    Replies: 1
    Last Post: March 8th 2009, 06:19 PM
  3. Infinite Sequences and Series
    Posted in the Calculus Forum
    Replies: 4
    Last Post: November 14th 2008, 02:28 PM
  4. Infinite Sequences
    Posted in the Calculus Forum
    Replies: 5
    Last Post: June 9th 2008, 07:09 AM
  5. infinite sequences
    Posted in the Calculus Forum
    Replies: 1
    Last Post: July 18th 2007, 08:10 PM

Search Tags


/mathhelpforum @mathhelpforum