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How do i find the value of p for this integration?

  1. Apr 13, 2009 #1
    using the integral, find the values of "p" so that the series converges

    [tex]\sum[/tex]1/(ln(n)*np) (n=2 to ∞)

    i had a similar question in which case i had
    [tex]\sum[/tex]1/(x*lnpx)

    [tex]\int[/tex]dx/(x*lnpx)
    and there i simply said t=lnx dt=dx/x

    [tex]\int[/tex]dt/tp

    and from there it was really simple, but in the case of this question i have been trying and trying and just cant get it
     
  2. jcsd
  3. Apr 13, 2009 #2
    Use the same substitution and write:

    [tex] n^p = e^{p \ln n} = e^{pt}[/tex]
     
  4. Apr 13, 2009 #3
    i tried that, but i got stuck, didnt think it was the right way to go, can you help me continue??
    for integration n=x

    [tex]\int[/tex]dx/(ln(x)*xp)
    t=ln(x)
    n=et
    dt=dx/x

    [tex]\int[/tex]dt/(t*et(p-1)
    now for conveniance i say q=p-1

    [tex]\int[/tex]dt/(t*etq)

    how do i continue this integration?
     
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