Convergence series problem. How to show that $$\sum_{n=3}^{\infty }\frac{1}{n(\ln n)(\ln \ln n)^p}$$ converges if and only if $p>1$ ?
By integral test, 
$$\sum_{n=3}^{\infty }\frac{1}{n(\ln n)(\ln \ln n)^p}$$
$$f(x)=\frac{1}{x(\ln x)(\ln \ln x)^P}$$
$$\int_{3}^{\infty }\frac{1}{x(\ln x)(\ln \ln x)^p}$$
I stucked at here.

One way to do it is to use the integral test.
