I have been trying for a week to prove a result from a textbook and have gotten nowhere. Please help.

I have the facts $\displaystyle q^{-\delta}$$\displaystyle logq$$\displaystyle $\rightarrow$$$\displaystyle $\infty$$ for each$\displaystyle $\delta$>0$ and I'm trying to prove for each $\displaystyle \epsilon>0$

$\displaystyle \sum_{q=1}^{\infty}((logq)/(q^{1+\epsilon}))<\infty$