Results 1 to 4 of 4

Math Help - Series: Converge of Diverge

  1. #1
    Junior Member
    Joined
    Jan 2010
    Posts
    72

    Series: Converge of Diverge

    Determine whether the series converges or diverges.

    Summation of (ln(k))/(k^3)
    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 WartonMorton View Post
    Determine whether the series converges or diverges.

    Summation of (ln(k))/(k^3)
    Since |\ln(x)|<x for x>1 the general general term is positive and <1/k^2 and you should be able to take it from there

    CB
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member
    Joined
    Apr 2009
    Posts
    678
    Thanks
    1
    Quote Originally Posted by WartonMorton View Post
    Determine whether the series converges or diverges.

    Summation of (ln(k))/(k^3)

    hint: i guess this should work (ln(k))/(k^3) < k/(k^3) = 1/k^2
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Super Member Failure's Avatar
    Joined
    Jul 2009
    From
    Zürich
    Posts
    555
    Quote Originally Posted by WartonMorton View Post
    Determine whether the series converges or diverges.

    Summation of (ln(k))/(k^3)
    Oh sure it converges. This is because \frac{\ln k}{k^3}=\frac{\ln k}{k}\cdot\frac{1}{k^2}, where the first factor \frac{\ln k}{k} converges to 0 for k\to\infty and the series \sum_k \frac{1}{k^2} of the second factor \frac{1}{k^2} also converges. - But maybe this way of arguing for convergence is a little too sloppy for your taste.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Does this series converge or diverge?
    Posted in the Differential Geometry Forum
    Replies: 2
    Last Post: May 6th 2010, 10:15 AM
  2. series - converge or diverge
    Posted in the Calculus Forum
    Replies: 1
    Last Post: November 10th 2009, 03:59 AM
  3. Does this series converge or diverge?
    Posted in the Calculus Forum
    Replies: 4
    Last Post: October 30th 2009, 08:57 AM
  4. Series converge or diverge?
    Posted in the Calculus Forum
    Replies: 4
    Last Post: June 1st 2008, 09:12 AM
  5. More on series converge or diverge?
    Posted in the Calculus Forum
    Replies: 2
    Last Post: May 21st 2008, 03:28 AM

Search Tags


/mathhelpforum @mathhelpforum