Series: comparison, ratio, root, Raabe, condensation, alternating, rearrangements

(a): the non-zero terms are $(-1{)}^k/\sqrt{2k+1}$, an alternating series with terms decreasing to 0 (Leibniz$).(b):\log (1+1/n^2)$ ~ $1/n^2$, comparison with a convergent p-series.