Results 1 to 6 of 6

Math Help - Sequences

  1. #1
    Super Member Showcase_22's Avatar
    Joined
    Sep 2006
    From
    The raggedy edge.
    Posts
    782

    Sequences

    I have another post about sequences but this question seems easier (hence why I posted it here!).

    However, "easier" is used relative to the other question I am stuck on (posted in Advanced Algebra).

    The problem is:

    Think of an example to show that the statement,

    if (a_n) \rightarrow 0 then \frac{1}{a_n} \rightarrow \infty

    is false, even if a_n \neq 0 for all n
    All the equations I have tried have failed. I can't think of a method to do this question properly =(

    Any ideas would be greatly appreciated!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,403
    Thanks
    1486
    Awards
    1
    \left[ {\frac{{\left( { - 1} \right)^n }}<br />
{n}} \right] \to 0

    But what about \frac{1}<br />
{{\left| {a_n } \right|}}?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Oct 2008
    Posts
    91
    Exactly.

    Think of a non-monotonic sequence that tends to zero, ie. that approaches zero from the "-ve and the +ve side".

    (-1)^n/n is a good example.
    Last edited by nmatthies1; October 10th 2008 at 12:31 PM.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Super Member Showcase_22's Avatar
    Joined
    Sep 2006
    From
    The raggedy edge.
    Posts
    782
    I thought of it that way but couldn't quite grasp the concept.

    I was trying sequences like a_n=\frac{sin n}{n}. Unfortunately this equals zero so it didn't work!

    thanks for the help guys!
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Super Member Showcase_22's Avatar
    Joined
    Sep 2006
    From
    The raggedy edge.
    Posts
    782
    lol, I didn''t see it!

    boy is my face red!

    So have you done the section about \pi yet? It's really confusing!

    (check my other thread in the advanced algebra section).
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Newbie
    Joined
    Oct 2008
    Posts
    3
    Not worry it happens to all of us.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Convergence in sequences of sequences
    Posted in the Differential Geometry Forum
    Replies: 4
    Last Post: October 19th 2010, 07:28 AM
  2. Sequences and the sequences' arithmetics
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: October 6th 2010, 09:31 PM
  3. Monotone sequences and Cauchy sequences
    Posted in the Differential Geometry Forum
    Replies: 3
    Last Post: March 21st 2009, 08:59 PM
  4. Sequences Q3
    Posted in the Calculus Forum
    Replies: 1
    Last Post: March 9th 2009, 05:08 AM
  5. Replies: 5
    Last Post: January 16th 2008, 04:51 PM

Search Tags


/mathhelpforum @mathhelpforum