Results 1 to 3 of 3

Math Help - infinite sequences problem

  1. #1
    Member
    Joined
    Aug 2008
    Posts
    249

    infinite sequences problem

    prove that:
    sqrt(1 + 2sqrt(1 + 3sqrt(1 +...))) = 3

    i am not sure how to start this. the only thing i can think of is squaring both sides:
    1 + 2sqrt(1 + 3sqrt(1 + 4sqrt(1 +...))) = 9
    sqrt(1 + 3sqrt(1 + 4sqrt(1 + 5sqrt(1 +...)))) = 4

    and so on. im not sure if this is the right way going about this. any hints?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    Joined
    Jun 2009
    Posts
    660
    Thanks
    133
    This is a problem attributed to Srinivasa Ramanujan (1887-1920).
    He apparently posed the problem in an Indian mathematics journal. After three further issues, (a period of six months), no solution was forthcoming so he presented the solution himself.
    A brief description of the solution can be found in Wikipedia, Nested Radicals.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member HappyJoe's Avatar
    Joined
    Sep 2010
    From
    Denmark
    Posts
    234
    A more thorough (and clever) proof can be found here: http://www.isibang.ac.in/~sury/ramanujanday.pdf
    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, 06:04 PM
  2. infinite sequences
    Posted in the Calculus Forum
    Replies: 1
    Last Post: March 8th 2009, 05:19 PM
  3. infinite sequences
    Posted in the Pre-Calculus Forum
    Replies: 3
    Last Post: December 10th 2008, 12:15 PM
  4. Infinite Sequences
    Posted in the Calculus Forum
    Replies: 5
    Last Post: June 9th 2008, 06:09 AM
  5. infinite sequences
    Posted in the Calculus Forum
    Replies: 1
    Last Post: July 18th 2007, 07:10 PM

Search Tags


/mathhelpforum @mathhelpforum