Results 1 to 5 of 5

Math Help - Sequences and their Limits

  1. #1
    Member
    Joined
    Feb 2008
    Posts
    102

    Sequences and their Limits

    Use Theorem 3 to show that the sequence 0.7, 0.77, 0.777, 0.7777, 0.77777, 0.777777, 0.7777777, ... has a limit.

    Theorem 3 is ...

    Suppose that the sequence  a_{k} is nondecresing and bounded above by a number A. That is,

     a_{1} \leq a_{2} \leq a_{3} \leq A

    Then  a_{k} converges to some finite limit a, with a  \leq A. Similarly, if  b_{k} is nonincreasing and bounded below by a number B, then  b_{k} converges to a finite limit b \geq  B.

    edit: How do I do the less than or equal to sign in LaTeX?
    Last edited by larson; April 20th 2008 at 06:51 PM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor Mathstud28's Avatar
    Joined
    Mar 2008
    From
    Pennsylvania
    Posts
    3,641
    Quote Originally Posted by larson View Post
    Use Theorem 3 to show that the sequence 0.7, 0.77, 0.777, 0.7777, 0.77777, 0.777777, 0.7777777, ... has a limit.

    Theorem 3 is ...

    Suppose that the sequence  a_{k} is nondecresing and bounded above by a number A. That is,

     a_{1} <,  a_{2} <  a_{3} < A

    Then  a_{k} converges to some finite limit a, with a < A. Similarly, if  b_{k} is nonincreasing and bounded below by a number B, then  b_{k} converges to a finite limit b > B.

    edit: How do I do the less than or equal to sign in LaTeX?
    /leq gives \leq just change / to \
    Follow Math Help Forum on Facebook and Google+

  3. #3
    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 larson View Post
    Use Theorem 3 to show that the sequence 0.7, 0.77, 0.777, 0.7777, 0.77777, 0.777777, 0.7777777, ... has a limit.

    Theorem 3 is ...

    Suppose that the sequence  a_{k} is nondecresing and bounded above by a number A. That is,

     a_{1} <,  a_{2} <  a_{3} < A

    Then  a_{k} converges to some finite limit a, with a < A. Similarly, if  b_{k} is nonincreasing and bounded below by a number B, then  b_{k} converges to a finite limit b > B.

    edit: How do I do the less than or equal to sign in LaTeX?
    you can use the first part of the theorem with A = 0. \bar{7} or A = 0.8
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor Mathstud28's Avatar
    Joined
    Mar 2008
    From
    Pennsylvania
    Posts
    3,641
    Quote Originally Posted by larson View Post
    Use Theorem 3 to show that the sequence 0.7, 0.77, 0.777, 0.7777, 0.77777, 0.777777, 0.7777777, ... has a limit.

    Theorem 3 is ...

    Suppose that the sequence  a_{k} is nondecresing and bounded above by a number A. That is,

     a_{1} <,  a_{2} <  a_{3} < A

    Then  a_{k} converges to some finite limit a, with a < A. Similarly, if  b_{k} is nonincreasing and bounded below by a number B, then  b_{k} converges to a finite limit b > B.

    edit: How do I do the less than or equal to sign in LaTeX?
    and I will give you a hint a_n=7\sum_{t=1}^{n}\cdot\bigg(\frac{1}{10}\bigg)^{  t}
    Last edited by Mathstud28; April 20th 2008 at 05:45 PM.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    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 Mathstud28 View Post
    /leq gives \leq just change / to \
    it suffices to type le, likewise, ge and ne for greater thank and not equal to respectively
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. limits of sequences
    Posted in the Advanced Statistics Forum
    Replies: 0
    Last Post: October 11th 2011, 10:33 AM
  2. Sequences and limits
    Posted in the Differential Geometry Forum
    Replies: 3
    Last Post: October 1st 2011, 07:00 PM
  3. Sequences - limits
    Posted in the Calculus Forum
    Replies: 6
    Last Post: October 1st 2008, 03:17 AM
  4. Limits and sequences
    Posted in the Calculus Forum
    Replies: 7
    Last Post: May 3rd 2008, 03:51 PM
  5. limits of sequences
    Posted in the Calculus Forum
    Replies: 4
    Last Post: April 4th 2007, 05:38 PM

Search Tags


/mathhelpforum @mathhelpforum