Results 1 to 4 of 4

Math Help - A limit of a sequence problem

  1. #1
    Member
    Joined
    Jan 2010
    Posts
    232

    A limit of a sequence problem

    Suppose that a_n\rightarrow L. Show that if a_n\leq M for all n, then L\leq M.
    Prove by contradiction and by choosing \epsilon =\frac{L-M}{2}.

    I have a standard proof for how to solve this, but not a contradictory proof (which is what I need). Can someone help with that?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,605
    Thanks
    1574
    Awards
    1
    If you assume that L>M then \epsilon=\frac{L-M}{2}>0 makes sense.
    That is by contradiction.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Jan 2010
    Posts
    232
    Quote Originally Posted by Plato View Post
    If you assume that L>M then \epsilon=\frac{L-M}{2}>0 makes sense.
    That is by contradiction.
    I'm afraid I don't fully understand how these things can be applied. The answer sounds right, but I can't slot it into my proof correctly. How exactly would one show this?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,605
    Thanks
    1574
    Awards
    1
    Quote Originally Posted by Runty View Post
    I'm afraid I don't fully understand how these things can be applied. How exactly would one show this?
    \left| {a_n  - L} \right| < \frac{{L - M}}<br />
{2} \Rightarrow M < \frac{{L + M}}<br />
{2} < a_n that is a contradiction.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. [SOLVED] Is there another way to do this sequence limit problem?
    Posted in the Calculus Forum
    Replies: 4
    Last Post: March 27th 2011, 09:43 AM
  2. Replies: 2
    Last Post: October 26th 2010, 10:23 AM
  3. Help on a convergent sequence limit problem
    Posted in the Calculus Forum
    Replies: 7
    Last Post: January 6th 2010, 07:04 PM
  4. Limit/Sequence
    Posted in the Calculus Forum
    Replies: 3
    Last Post: April 15th 2008, 06:48 PM
  5. Limit of sequence
    Posted in the Calculus Forum
    Replies: 1
    Last Post: March 19th 2008, 08:13 PM

Search Tags


/mathhelpforum @mathhelpforum