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: Determine if series converges

  1. May 17, 2010 #1
    1. The problem statement, all variables and given/known data

    Is the series convergent

    1) [tex]\sum[/tex]1/(n^2 * ln n)

    and 2) which value of p does the series converge. [tex]\sum[/tex] 1/(n*(ln n)^p)


    3. The attempt at a solution

    1)

    I cannot see how the root method ([tex]\sqrt[n]{Cn}[/tex]) would work, or the ratio test would work (cn+1)/cn

    Unless you use the limit test and lim 1/(n^2 * ln n) = 1/infinity = 0 therefore the series converges. I didnt think that question would be that easy though.

    2) Similiar to the first wouldn't it just be if P > 1.
     
  2. jcsd
  3. May 17, 2010 #2

    Mark44

    Staff: Mentor

    The test you are thinking of, I believe, is the nth term test for divergence. If lim an != 0, the series diverges. You cannot use this test to conclude a series converges.

    A test that might be useful in this problem is the comparison test.
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook