Results 1 to 5 of 5

Math Help - Converges, Diverges, Can't Tell

  1. #1
    Newbie
    Joined
    Sep 2008
    From
    Denver, CO in the beautiful Rocky Mountains
    Posts
    23

    Converges, Diverges, Can't Tell

    Answer with converges, diverges, or can't tell

    If the \lim a_k=0, then \sum a_k=0

    So, since the a_k isn't an absolute value, doesn't that mean that I can't tell if it diverges or converges? Or is there some other rule that I'm forgetting when it comes to determining converging/diverging?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Global Moderator

    Joined
    Nov 2005
    From
    New York City
    Posts
    10,616
    Thanks
    9
    Quote Originally Posted by kl.twilleger View Post
    Answer with converges, diverges, or can't tell

    If the \lim a_k=0, then \sum a_k=0

    So, since the a_k isn't an absolute value, doesn't that mean that I can't tell if it diverges or converges? Or is there some other rule that I'm forgetting when it comes to determining converging/diverging?
    Let a_n = \tfrac{1}{n}. Then \lim a_n = 0 yet \Sigma_{n\geq 1}a_n = \infty.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Sep 2008
    From
    Denver, CO in the beautiful Rocky Mountains
    Posts
    23
    So then it diverges to infinity? Or do I not know?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,649
    Thanks
    1597
    Awards
    1
    Quote Originally Posted by kl.twilleger View Post
    So then it diverges to infinity? Or do I not know?
    The series may or may not converge.
    Examples:
    \left( {\frac{1}{n}} \right) \to 0\;\& \;\sum\limits_{n = 1}^\infty  {\frac{1}{n}}\mbox{  diverges.}

    \left( {\frac{1}{n^2}} \right) \to 0\;\& \;\sum\limits_{n = 1}^\infty  {\frac{1}{n^2}}\mbox{  converges.}
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor Mathstud28's Avatar
    Joined
    Mar 2008
    From
    Pennsylvania
    Posts
    3,641
    Quote Originally Posted by kl.twilleger View Post
    Answer with converges, diverges, or can't tell

    If the \lim a_k=0, then \sum a_k=0

    So, since the a_k isn't an absolute value, doesn't that mean that I can't tell if it diverges or converges? Or is there some other rule that I'm forgetting when it comes to determining converging/diverging?
    Are you trying to remember the n-th term test for divergence, which roughly states that if you have \sum{a_n} for which a_{n} does not converge to zero then your series diverges. If a_n does converge to zero this says nothing of the series convergence or divergence as can be shown by TPH or Plato's or a hundred million other cases where a_n tends to zero but some series converge some don't[/tex]
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Converges and Diverges
    Posted in the Pre-Calculus Forum
    Replies: 7
    Last Post: May 20th 2010, 04:42 PM
  2. Converges or Diverges
    Posted in the Calculus Forum
    Replies: 3
    Last Post: November 13th 2008, 01:03 PM
  3. Converges or Diverges?
    Posted in the Calculus Forum
    Replies: 10
    Last Post: July 19th 2008, 12:10 AM
  4. converges or diverges
    Posted in the Calculus Forum
    Replies: 3
    Last Post: April 25th 2008, 11:21 AM
  5. diverges or converges?
    Posted in the Calculus Forum
    Replies: 1
    Last Post: January 16th 2007, 08:12 PM

Search Tags


/mathhelpforum @mathhelpforum