Integral for Multiple Natural Logs

[Dragon M.]

Homework Statement

I need to find whether or not the Ʃ1/(n(ln n)(ln(ln(n)))) (from 2 to infinity) converges or diverges using the Integral test. I think the best question to ask is where to start with the integral?

Homework Equations

None.

The Attempt at a Solution

I've tried integrating by parts, but I can't find du or v for 1/(lnx)ln(ln(x)). Is there a way to simplify this into a more friendly form?

 

[HallsofIvy]

If you let u= ln(ln(x)) then $du= (1/ln(x))(1/x)dx$.