Results 1 to 3 of 3

Math Help - convergent sequence

  1. #1
    Newbie
    Joined
    Jul 2007
    Posts
    19

    convergent sequence

    a= (n^2-5n+6)/(n^2+n+1)

    using the definition only prove the sequence(a) is convergent and find its limit?

    what does this prove by definition means? is it same as when proving a limit?

    any help is welcome. thanks
    Follow Math Help Forum on Facebook and Google+

  2. #2
    is up to his old tricks again! Jhevon's Avatar
    Joined
    Feb 2007
    From
    New York, USA
    Posts
    11,663
    Thanks
    3
    Quote Originally Posted by Dili View Post
    a= (n^2-5n+6)/(n^2+n+1)

    using the definition only prove the sequence(a) is convergent and find its limit?

    what does this prove by definition means? is it same as when proving a limit?

    any help is welcome. thanks
    Definition: Let \{ a_n \} be a sequence of real numbers. We say " \{ a_n \} converges to L" if for every \epsilon > 0, there exists an N \in \mathbb {N}, such that n > N implies |a_n - L |< \epsilon. We write \lim_{n \to \infty}a_n = L when this happens.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Global Moderator

    Joined
    Nov 2005
    From
    New York City
    Posts
    10,616
    Thanks
    10
    Quote Originally Posted by Jhevon View Post
    Definition: Let \{ a_n \} be a sequence of real numbers. We say " \{ a_n \} converges to L" if for every \epsilon > 0, there exists an N \in \mathbb {N}, such that n > N implies |a_n - L |< \epsilon. We write \lim_{n \to \infty}a_n = L when this happens.
    It seems the poster is asking how to use this definition to prove his result. Not the actual definition.

    a= (n^2-5n+6)/(n^2+n+1)
    Experimentation suggests that \lim a_n = 1. We want to show |a_n - 1| can be made as small as we want. Meaning,
    \left| \frac{n^2 - 5n+6}{n^2+n+1} - 1 \right| = \left| \frac{-6n+5} {n^2+n+1} \right| \leq \frac{6n+5}{n^2+n+1} \leq \frac{6n+5n}{n^2} = \frac{11}{n}

    What I wrote is a hint, complete the arugment thyself.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Convergent sequence
    Posted in the Differential Geometry Forum
    Replies: 4
    Last Post: October 15th 2010, 06:27 AM
  2. convergent sequence
    Posted in the Differential Geometry Forum
    Replies: 7
    Last Post: February 27th 2010, 12:59 PM
  3. convergent sequence
    Posted in the Differential Geometry Forum
    Replies: 2
    Last Post: December 30th 2009, 10:32 PM
  4. Convergent Sequence
    Posted in the Differential Geometry Forum
    Replies: 2
    Last Post: August 11th 2009, 08:42 AM
  5. Convergent sequence
    Posted in the Differential Geometry Forum
    Replies: 6
    Last Post: July 7th 2009, 05:11 PM

Search Tags


/mathhelpforum @mathhelpforum