Which one $is$ true about the series ${\displaystyle \underset{n=1}{\overset{}{}}}ln(\frac{1}{n})?$

$(a)$ The series $is$ convergent $by$ the ratio test.

$(b)$ The series converges conditionally.

$(c)\underset{n}{lim}ln(\frac{1}{n})=$

$(d)$ The terms $of$ the corresponding sequence are increasing.

$(e)$ The series diverges $by$ the $n^{th}-$term test because the $limitof$ the $n^{th}-$term $is-.$

Which one $is$ true about the series ${\displaystyle \underset{n=1}{\overset{}{}}}(\frac{n}{n+1}{)}^{n^2}?$

$(a)$ The series $is$ inconclusive $by$ the root test.

$(b)$ The series $is$ convergent $by$ the root test.

$(c)$ The series $is$ divergent $by$ the ratio test.

$(d)$ The $limitof$ the corresponding sequence $is1.$

$(e)$ The series $is$ bounded below $bye.$

Which one $is$ true about the series ${\displaystyle \underset{n=1}{\overset{}{}}}\frac{(3n)!}{3^{3n}}?$

$(a)$ The series $is$ inconclusive $by$ the root test.

$(b)$ The series $is$ convergent $by$ the root test.

$(c)$ The series $is$ divergent $by$ the ratio test.

$(d)$ The $limitof$ the corresponding sequence $is1.$

$(e)$ The series $is$ bounded above $by{3}^{123}$