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: Have i done this right?

  1. Apr 14, 2009 #1
    i need to tell if the following sequence converges or diverges

    [tex]\sum[/tex](-1)n-1lnp(n)/n {p>0}
    (n from 1 to infinity)

    what i think i need to do is take the positive version of this series

    [tex]\sum[/tex]lnp(n)/n {p>0}
    (n from 1 to infinity)
    if the positive series converges than the original must also, if not i can use leibnitz to tell me its behaviour

    the problem it the "p", surely {p>0} is not enough information, do i not need to know if p>1 or p<1???

    i can integrate [tex]\int[/tex](lnp(x)/x)dx ===> t=lnx dt=dx/x

    =tp+1/(p+1) =...


    if P>-1 [tex]\sum[/tex]lnp(n)/n diverges
    if P<-1 [tex]\sum[/tex]lnp(n)/n converges
    if p=-1 [tex]\sum[/tex]lnp(n)/n diverges

    but i am told that {p>0} therefor i am only left with one option
    if P>-1 [tex]\sum[/tex]lnp(n)/n diverges

    so now i need to check if:
    - lim An = 0
    - An+1< An
    Last edited: Apr 14, 2009
  2. jcsd
  3. Apr 14, 2009 #2
    lim An= ln^p(n)/n = 0

    so now how do i prove that An > A(n+1)
    Last edited: Apr 14, 2009
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook