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How do i solve this usung integration?

  1. Apr 16, 2009 #1
    find the values for "p" so that the following series converges:


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


    the question actually asks to use integration to find the value of "p", i have not managed to integrate this at all but what i have manages is the following:

    i found a series which is samller than An,
    Bn=1/np, making An=Bn/ln(n),
    i think that since the relation of An and Bn is not dependant on "p", if i find the p so that Bn converges i can solve the problem
    therefore P>1 An converges,

    BUT they asked specifically to use integration to find the value of p,
    what i tried so far is

    [tex]\int[/tex]dx/(ln(x)*xp)
    t=ln(x)
    x=et
    dt=dx/x
    [tex]\int[/tex]dx/(x*ln(x)*xp-1)=[tex]\int[/tex]dt/t*et(p-1)

    from here i am totally stuck, dont know how to continue, and for that matter not sure i am on the right track!
     
    Last edited: Apr 16, 2009
  2. jcsd
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