Results 1 to 2 of 2

Math Help - Finite Continued Fraction Question

  1. #1
    Member
    Joined
    Nov 2008
    Posts
    152

    Finite Continued Fraction Question

    Show that every rational number has exactly two finite simple continued fraction expansions.

    (Does this have something to do with how you handle the end of the continued fraction?)
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Mar 2010
    From
    Florida
    Posts
    3,093
    Thanks
    5
    \displaystyle \frac{225}{157}

    This can be represented as <b_0;b_1,b_2,\cdots, b_k> \ \mbox{and} \ <b_0;b_1,b_2,\cdots, b_k-1,1>

    Therefore, our fraction can be represented like

    \displaystyle <1; 2,3,4,5>

    \displaystyle 1+\frac{1}{2+\frac{1}{3+\frac{1}{4+\frac{1}{5}}}}

    or

    \displaystyle <1;2,3,4,4,1>

    \displaystyle 1+\frac{1}{2+\frac{1}{3+\frac{1}{4+\frac{1}{4+\fra  c{1}{1}}}}}}
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Continued fraction.
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: January 27th 2011, 09:54 AM
  2. Value of a continued fraction.
    Posted in the Algebra Forum
    Replies: 1
    Last Post: March 11th 2009, 10:12 AM
  3. continued fraction help ?
    Posted in the Number Theory Forum
    Replies: 2
    Last Post: May 10th 2008, 08:10 AM
  4. finite continued fractions ?
    Posted in the Number Theory Forum
    Replies: 3
    Last Post: May 5th 2008, 10:02 PM
  5. continued fraction
    Posted in the Discrete Math Forum
    Replies: 3
    Last Post: February 27th 2006, 04:37 PM

Search Tags


/mathhelpforum @mathhelpforum