Results 1 to 4 of 4

Math Help - Sum of oscillating sequences

  1. #1
    Member
    Joined
    Oct 2009
    From
    United States
    Posts
    169

    Sum of oscillating sequences

    Find two oscillating sequences such that the sum of those two sequences diverges to infinity or to minus infinity, if possible. I have been unable to find two such sequences. It is easy enough to find two oscillating sequences who sum converges, but not diverges. Any ideas? Thanks.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Member
    Joined
    Jul 2009
    Posts
    120
    take two sequences to be the same diverging oscillating sequence?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor Bruno J.'s Avatar
    Joined
    Jun 2009
    From
    Canada
    Posts
    1,266
    Thanks
    1
    Awards
    1
    Quote Originally Posted by zzzhhh View Post
    take two sequences to be the same diverging oscillating sequence?
    But then you get an alternating sequence, which doesn't converge to infinity.

    How about :

    -1, 2, -1/3, 4, -1/5, 6, ...

    and

    1, -1/2, 3, -1/4, 5, -1/6, ...
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Newbie
    Joined
    Feb 2010
    From
    Berlin
    Posts
    16
    By "oscillating" I assume that you mean alternating, i.e., the sign changes like a_n > 0 \Rightarrow a_{n+1}<0.

    Think about what you want to do: a single alternating sequence can diverge, but it cannot have \infty or -\infty as a limit, because of the sign changes. The idea would be to find a sequence (a_n) whose subsequence of even terms approach \infty but its odd subsequence (of negative terms) remain bounded. Then find a sequence (b_n) whose odd terms approach \infty but its even terms (here, negative as per requirement) remain bounded. The sum a_n + b_n should do what you want.

    If this is too abstract, see Bruno J's suggestion.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. oscillating particle problem
    Posted in the Advanced Applied Math Forum
    Replies: 2
    Last Post: August 19th 2010, 11:35 PM
  2. Complex number - Oscillating system
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: August 11th 2009, 11:28 PM
  3. Particle oscillating on a fixed string
    Posted in the Calculus Forum
    Replies: 0
    Last Post: June 2nd 2009, 09:08 AM
  4. Finding the equation of an oscillating mass
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: March 28th 2009, 06:38 AM
  5. Oscillating spring measurements?
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: March 8th 2009, 02:45 PM

Search Tags


/mathhelpforum @mathhelpforum