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: For what values of p does the series converge?

  1. Nov 7, 2007 #1
    1. The problem statement, all variables and given/known data
    For what values of p does the series converge?

    2. Relevant equations
    Σn=2 1/(n^p)(ln n)

    3. The attempt at a solution
    So far, all that is available to me is the integral test, the comparison test and the limit comparison test.

    So using the comparison test. 1/(n^p)(ln n) < 1/n^p

    1/n^p is a p series and only converges when p>1. So it converges.

    But this doesn't feel right :(
  2. jcsd
  3. Nov 7, 2007 #2


    User Avatar
    Homework Helper

    This is fine: the comparison of terms is valid for n > 1 (so the summation in the series would have to start at n = 2).

    In having looked at a fair number of these p-series related problems, I've come to think of the contribution of a (ln n) factor as equivalent to adding zero to the p exponent when conducting the "p-test"; the natural logarithm in such series seems to make a negligible contribution to the convergence of the series.
  4. Nov 7, 2007 #3
    ah i meant to add in so it converges for p>1

    its just that all the p series problems usually end up with p>1 XD
  5. Nov 7, 2007 #4


    User Avatar
    Homework Helper

    That's largely because of the problems authors tend to choose for courses making a first pass through material on infinite series. Not all p-series one may encounter turn out that way... ;-)
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook