# How do i solve this usung integration?

1. Apr 16, 2009

### Dell

find the values for "p" so that the following series converges:

$$\sum$$ 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

$$\int$$dx/(ln(x)*xp)
t=ln(x)
x=et
dt=dx/x
$$\int$$dx/(x*ln(x)*xp-1)=$$\int$$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