# Convergence of sequence with log

1. Sep 25, 2011

### l888l888l888

1. The problem statement, all variables and given/known data
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.

2. Relevant equations

3. 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)...

2. Sep 25, 2011

### Dick

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

3. Sep 25, 2011

### l888l888l888

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

4. Sep 25, 2011

### Dick

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?