Results 1 to 2 of 2

Math Help - Analysis-Sequences

  1. #1
    Newbie
    Joined
    Mar 2013
    From
    sacramento
    Posts
    7

    Analysis-Sequences

    Suppose that (sn )converges to s. Prove that (sn )2 converges to s directly without using the product formula.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,605
    Thanks
    1574
    Awards
    1

    Re: Analysis-Sequences

    Quote Originally Posted by leonhart View Post
    Suppose that (sn )converges to s. Prove that (sn )2 converges to s directly without using the product formula.

    First you have miss-stated it: (s_n^2)\to s^2.

    Note that |s_n^2-s^2|=|s_n-s||s_n+s|.

    Because (s_n) is bounded, |s_n+s| has a bound. Call its bound, B+1.

    Because (s_n)\to s you can make |s_n-s|<\frac{\epsilon}{B+1}.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Analysis. Sequences.
    Posted in the Pre-Calculus Forum
    Replies: 5
    Last Post: March 30th 2010, 01:42 PM
  2. Real Analysis - Sequences 3
    Posted in the Differential Geometry Forum
    Replies: 3
    Last Post: February 16th 2010, 02:18 PM
  3. Real Analysis - Sequences
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: February 15th 2010, 06:36 PM
  4. Real Analysis - Sequences #3
    Posted in the Calculus Forum
    Replies: 1
    Last Post: January 20th 2009, 01:35 PM
  5. Analysis: Sequences
    Posted in the Calculus Forum
    Replies: 1
    Last Post: November 16th 2008, 02:43 PM

Search Tags


/mathhelpforum @mathhelpforum