1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Converging or diverging 1/ln(n)

  1. Jan 9, 2010 #1
    Determine if the series n=2 to inf. of 1/ln(n) converges or diverges

    Ok so first I tried the limit test (the simple one) and found that it was 0 which was not helpful at all. Then I tried the integral test. It came out to be (integral)1/ln(n)=n/ln(n) + n/(ln(n))^2 + 2(integral from 2 to infin.) 1/(ln(n))^3. I was thinking of possibly doing a direct comparison test, but I have no clue what to compare it to. So then I tried the ratio test. That also failed, because the limit of the absolute value of the ratio was equal to 1 thus inconclusive and leaving me back where I started.

    I have no idea how else to approach this problem. I am hoping that I maybe just messed up my integration. If anyone has a clue how to approach this that would be great.
  2. jcsd
  3. Jan 9, 2010 #2
    Try comparing it with the harmonic series
  4. Jan 9, 2010 #3
    ahhhh. Just to check. When I do a direct comparison to the harmonic series (which diverges) 1/ln(n) is larger so it must also converge. Is this right or have I been staring at this problem long enough that my logic is swiss cheese?
  5. Jan 9, 2010 #4
    Check the criteria for the comparison test again, you've made one mistake.
  6. Jan 9, 2010 #5
    The only criteria I have for the Direct Comparison test is that "if a series is less than or equal to a converging series then it also converges." and "if it is greater than a diverging series it also diverges." Am I missing something?
  7. Jan 9, 2010 #6
    o wait....duh since harmonic diverges and the 1/lnn is larger it must diverge. that was stupid on my part
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook