Results 1 to 4 of 4

Math Help - combine convegence question..

  1. #1
    MHF Contributor
    Joined
    Nov 2008
    Posts
    1,401

    combine convegence question..

    prove that if An->a and An-Bn->0 then Bn->a

    ??
    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 transgalactic View Post
    prove that if An->a and An-Bn->0 then Bn->a

    ??
    http://www.mathhelpforum.com/math-he...-question.html

    ??
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,790
    Thanks
    1687
    Awards
    1
    If \varepsilon > 0 then \left( {\exists N} \right)\left[ {n \geqslant N \Rightarrow \left| {A_n - a} \right| < \frac{\varepsilon }{2}\,\& \,\left| {A_n - B_n } \right| < \frac{\varepsilon }{2}} \right].
    So \left| {B_n - a} \right| \leqslant \left| {B_n - A_n } \right| + \left| {A_n - a} \right| < \varepsilon .
    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 Plato View Post
    If \varepsilon > 0 then \left( {\exists N} \right)\left[ {n \geqslant N \Rightarrow \left| {A_n - a} \right| < \frac{\varepsilon }{2}\,\& \,\left| {A_n - B_n } \right| < \frac{\varepsilon }{2}} \right].
    So \left| {B_n - a} \right| \leqslant \left| {B_n - A_n } \right| + \left| {A_n - a} \right| < \varepsilon .
    Did I screw up in my proof? Yours looks exactly the same?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Radius of convegence
    Posted in the Calculus Forum
    Replies: 1
    Last Post: April 26th 2009, 10:18 AM
  2. Replies: 1
    Last Post: April 1st 2009, 06:32 AM
  3. series convegence
    Posted in the Calculus Forum
    Replies: 1
    Last Post: April 1st 2009, 05:19 AM
  4. convegence question..
    Posted in the Calculus Forum
    Replies: 2
    Last Post: December 10th 2008, 01:00 PM
  5. Replies: 2
    Last Post: October 30th 2007, 07:09 AM

Search Tags


/mathhelpforum @mathhelpforum