Results 1 to 2 of 2

Math Help - sequence

  1. #1
    Member
    Joined
    Aug 2008
    Posts
    172

    sequence

    Prove that if  x_n \to x and x>0 , then there is  k \in N such that  \frac {x}{2} < x_n < \frac{3x}{2}, \forall n \geq k
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor Bruno J.'s Avatar
    Joined
    Jun 2009
    From
    Canada
    Posts
    1,266
    Thanks
    1
    Awards
    1
    By definition, since x_n converges to x, we can find k such that |x_n-x|<\frac{x}{2} whenever n\geq k, i.e.

    \frac{-x}{2}<x_n-x<\frac{x}{2}

    whenever n\geq k. Adding x throughout this inequality we get

    \frac{x}{2}<x_n<\frac{3x}{2}

    whenever n\geq k.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 2
    Last Post: August 24th 2010, 02:10 AM
  2. Replies: 0
    Last Post: July 4th 2010, 12:05 PM
  3. Replies: 2
    Last Post: March 1st 2010, 11:57 AM
  4. sequence membership and sequence builder operators
    Posted in the Discrete Math Forum
    Replies: 0
    Last Post: June 4th 2009, 03:16 AM
  5. Replies: 12
    Last Post: November 15th 2006, 12:51 PM

Search Tags


/mathhelpforum @mathhelpforum