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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

    [tex]\int[/tex]tpdt
    =tp+1/(p+1) =...

    ...lnp+1(n)|[tex]^{infinity}_{1}[/tex]

    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
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