Investigate the convergence of the series (i) $\sum_{n=2}^{\infty} \frac{1}{n^{p}(\log n)^{q}}$ (ii) $\sum_{n=3}^{\infty} \frac{1}{n(\log \log n)^{r}}$

for positive real values of $p, q$ and $r$.

[You may assume that for any positive real value of $\alpha, \log n<n^{\alpha}$ for $n$ sufficiently large. You may assume standard tests for convergence, provided that they are clearly stated.]