(A) Show that for any positive rational number $r$, the sequence $\left\{\frac{\log n}{n^r} : n \geq 1\right\}$ is bounded. (B) Show that the series $$\sum_{n \geq 10} \frac{(\log n)^2 (\log \log n)}{n^2}$$ is convergent.
(A) Show that for any positive rational number $r$, the sequence $\left\{\frac{\log n}{n^r} : n \geq 1\right\}$ is bounded.\\
(B) Show that the series
$$\sum_{n \geq 10} \frac{(\log n)^2 (\log \log n)}{n^2}$$
is convergent.