# Math Help - Convergence with multiple variables

1. ## Convergence with multiple variables

Find the positive values of $p$ for which the series converges:

$\sum_{n=2}^{\infty} \frac {1}{n (\ln n)^p}$

2. Hello,

Take a look at this : Bertrand Series

3. ## OK go through with the integral test

$\int_1^{\infty}\frac{1}{n\ln(n)^{p}}dn$= $\frac{(\ln(n))^{-p+1}}{-p+1}+C$ and I think you can see where to go from there...just remmber that it must converge(the integral) for the series to converge..oh yeah and if $p=1$ then the antiderivative is $\ln(\ln(n))$ +C

4. But you did it from 1 to infinity, and it is 2 to infinity.......

5. Do it when $n=2$ and apply the integral test.

6. Lemme check my answer, is it when p > 1?

7. ## Yes

I think thats right