Results 1 to 2 of 2

Math Help - infinite series convergence theorems

  1. #1
    Junior Member
    Joined
    Oct 2009
    Posts
    39

    infinite series convergence theorems

    Let S be an infinite series.
    Let S+ be the infinite series which consists of the positive terms in S (the nth term of S+ is 0 if the nth term of S is negative, otherwise the terms of S+ = the terms of S)
    Let S- be the infinite series which consists of the negative terms of S.

    From my text I have gathered that:

    S+ and S- both converge <=> S is absolutely convergent
    S+ and S- both diverge <= S is conditionally convergent
    only one of S+ and S- converges, the other diverges => S is divergent

    But it is not clear in the text whether

    S+ and S- both diverge => S is conditionally convergent
    only one of S+ and S- converges, the other diverges <= S is divergent


    ie. if both S+ and S- diverge, can S diverge?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Senior Member
    Joined
    Feb 2010
    Posts
    422
    What about 1-2+3-4+5-\cdots or \frac12 +\frac13 - \frac13 + \frac14 + \frac15-\frac15+\cdots?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Convergence of Infinite Series
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: March 6th 2011, 02:46 AM
  2. Convergence of Infinite Series
    Posted in the Calculus Forum
    Replies: 4
    Last Post: June 8th 2010, 03:09 PM
  3. Replies: 7
    Last Post: October 12th 2009, 10:10 AM
  4. convergence of an infinite series
    Posted in the Calculus Forum
    Replies: 1
    Last Post: November 17th 2008, 04:54 AM
  5. Convergence of infinite series
    Posted in the Calculus Forum
    Replies: 2
    Last Post: April 12th 2008, 02:11 PM

Search Tags


/mathhelpforum @mathhelpforum