Results 1 to 3 of 3

Math Help - [SOLVED] does the series converge

  1. #1
    Member
    Joined
    Jan 2009
    From
    Kingston, PA
    Posts
    96

    Question [SOLVED] does the series converge

    In my calc 3 class were using the divergence and integral test to determine wheter series converge or diverge. Im drawing blanks on this problem !

    K / ln(k+1)
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Jester's Avatar
    Joined
    Dec 2008
    From
    Conway AR
    Posts
    2,392
    Thanks
    56
    Quote Originally Posted by nikie1o2 View Post
    In my calc 3 class were using the divergence and integral test to determine wheter series converge or diverge. Im drawing blanks on this problem !

    K / ln(k+1)
    If

    \lim_{x \to \infty} \frac{x}{\ln(x+1)} \ne 0 the series diverges. Use L'Hopital's rule to show this doesn't happen, i.e.

    \lim_{x \to \infty} \frac{x}{\ln (x+1)} \to \infty
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,914
    Thanks
    779
    Hello, nikie1o2!

    Converge or diverge? . S \;=\;\sum^{\infty}_{k=1} \frac{k}{\ln(k+1)}
    I'd use the Comparison Test . . .


    We have: . \ln(k+1) \:<\:k+1

    Then: . \frac{\ln(k+1)}{k} \:<\:\frac{k+1}{k}\quad \text{ for positive }k

    Invert: . \frac{k}{\ln(k+1)} \:>\:\frac{k}{k+1}

    Take sums: . S \;=\;\sum^{\infty}_{k=1}\frac{k}{\ln(k+1)} \;> \;\sum^{\infty}_{k=1}\frac{k}{k+1}


    Now: . \sum^{\infty}_{k=1}\frac{k}{k+1} \;>\;\sum^{\infty}_{k=1}\frac{1}{k+1} \;=\;\frac{1}{2} + \frac{1}{3} + \frac{1}{4} + \hdots divergent Harmonic Series


    Hence: . S \:>\:\text{(divergent series)}

    Therefore: . S diverges.

    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 4
    Last Post: June 26th 2010, 08:04 AM
  2. [SOLVED] Series - Converge or diverge
    Posted in the Calculus Forum
    Replies: 5
    Last Post: June 7th 2010, 07:26 PM
  3. [SOLVED] Series- converge?
    Posted in the Calculus Forum
    Replies: 9
    Last Post: December 5th 2009, 10:04 PM
  4. Series converge
    Posted in the Calculus Forum
    Replies: 7
    Last Post: November 27th 2009, 09:21 AM
  5. What does the series converge to?
    Posted in the Calculus Forum
    Replies: 8
    Last Post: May 16th 2008, 12:56 PM

Search Tags


/mathhelpforum @mathhelpforum