Find the positive values of $\displaystyle p$ for which the series converges:
$\displaystyle \sum_{n=2}^{\infty} \frac {1}{n (\ln n)^p}$
Hello,
Take a look at this : Bertrand Series
$\displaystyle \int_1^{\infty}\frac{1}{n\ln(n)^{p}}dn$=$\displaystyle \frac{(\ln(n))^{-p+1}}{-p+1}+C$ 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 $\displaystyle p=1$ then the antiderivative is $\displaystyle \ln(\ln(n))$ +C