Results 1 to 2 of 2

Math Help - rearranged series

  1. #1
    Junior Member
    Joined
    Sep 2009
    Posts
    53

    rearranged series

    Let the summation from k=1 to infinity of a_k be a nonabsolutely convergent series. Show that there is a rearrangement of this series so that the sequence of a partial sums of the rearranged series converges to infinity.

    Also, show that there is a rearrangement of this series so that the sequence of partial sums of the rearranged series is bounded but does not converge.

    Thanks!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by friday616 View Post
    Let the summation from k=1 to infinity of a_k be a nonabsolutely convergent series. Show that there is a rearrangement of this series so that the sequence of a partial sums of the rearranged series converges to infinity.

    Also, show that there is a rearrangement of this series so that the sequence of partial sums of the rearranged series is bounded but does not converge.

    Thanks!
    Since the series is not absolutely convergent (but presumably convergent) the sums of the sub-sequences of positive and negative terms must diverge.

    CB
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 3
    Last Post: September 29th 2010, 06:11 AM
  2. formula rearranged
    Posted in the Algebra Forum
    Replies: 4
    Last Post: April 25th 2010, 09:04 AM
  3. formula rearranged
    Posted in the Calculus Forum
    Replies: 2
    Last Post: April 25th 2010, 08:03 AM
  4. Replies: 0
    Last Post: January 26th 2010, 08:06 AM
  5. Replies: 1
    Last Post: May 5th 2008, 09:44 PM

Search Tags


/mathhelpforum @mathhelpforum