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

  • Thread starter Dell
  • Start date
  • #1
590
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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
 

Answers and Replies

  • #2
525
6
Use the same substitution and write:

[tex] n^p = e^{p \ln n} = e^{pt}[/tex]
 
  • #3
590
0
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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