Results 1 to 4 of 4

Math Help - alternating serries test

  1. #1
    Senior Member
    Joined
    Jun 2009
    Posts
    251

    alternating serries test

    Is the convererse true for the alternating series test?
    For example if b_{n+1} \leq b_n is not true and \lim_{n\to0} b_n=0 is not true, does that mean the series diverges?
    Last edited by Chris L T521; August 1st 2009 at 07:31 PM. Reason: fixed LaTeX
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    11,621
    Thanks
    426
    Quote Originally Posted by superdude View Post
    Is the convererse true for the alternating series test?
    For example if b_{n+1} \le b_n is not true and \lim_{n\to \infty}b_n=0 is not true, does that mean the series diverges?

    edited the limit and latex errors ... am I correct?
    any series whose nth term does not go to zero diverges.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by superdude View Post
    Is the convererse true for the alternating series test?
    For example if b_{n+1} \leq b_n is not true and \lim_{n\to0} b_n=0 is not true, does that mean the series diverges?
    If \lim_{n\to 0} b_n=0 is not true then the sequence of partial sums cannot converge.

    CB
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by superdude View Post
    Is the convererse true for the alternating series test?
    For example if b_{n+1} \leq b_n is not true and \lim_{n\to0} b_n=0 is not true, does that mean the series diverges?
    if b_{n+1} \leq b_n is not true but \lim_{n\to0} b_n=0 is true then the series may converge.


    Consider:

    S=\sum_{n=0}^{\infty} a_n

    a_n = \begin{cases} (1/3)^n & n \text{ even} \\ -(1/2)^{n-1} & n \text{ odd} \end{cases}

    CB
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Alternating Series Test
    Posted in the Calculus Forum
    Replies: 3
    Last Post: March 26th 2011, 03:37 PM
  2. alternating series test
    Posted in the Calculus Forum
    Replies: 1
    Last Post: November 10th 2009, 10:04 PM
  3. Alternating series test
    Posted in the Differential Geometry Forum
    Replies: 0
    Last Post: October 1st 2009, 10:29 PM
  4. alternating series test
    Posted in the Calculus Forum
    Replies: 2
    Last Post: March 29th 2009, 01:54 PM
  5. Alternating Series Test
    Posted in the Calculus Forum
    Replies: 1
    Last Post: February 16th 2009, 01:57 PM

Search Tags


/mathhelpforum @mathhelpforum