Convergence of sequence with log

[l888l888l888]

Homework Statement

prove that the series summation from n=3 to infinity of (1/(n*log(n)*(log(log(n))^p)) diverges if 0<p<=1 and converges for p>1.

Homework Equations

The Attempt at a Solution

2^n*a(2^n)= 1/(log(2^n)*(log(log(2^n))^p)). this is similar to the summation from n=2 to infinity of 1/(n(logn^p)) if we let n = log(2^n)...

 

[Dick]

Try an integral test. Do the integral with a u substitution. What comes to mind?

 

[l888l888l888]

we r not allowed to use integral tests. this is an analysis 1 class

 

[Dick]

we r not allowed to use integral tests. this is an analysis 1 class

I'm kind of surprised you don't have the integral test. It looks like you are trying to use the Cauchy condensation test. That's fine, but eventually you are going to get down to summing 1/n^p. Don't you need an integral test for that? Or were you just given that it diverges for p<=1 and converges for p>1?