Consider the series ${\displaystyle \underset{n=1}{\overset{}{}}}(-1{)}^{n+1}{a}_n,$ where $a_n>\frac{1}{n}$ for all $n$ and the sequence $\{a_n\}$ decreases with limit $0.$ Which of the following statements is true?

$($A$)$ The series converges absolutely$.$

The series converges conditionally.

The series diverges.

$($D$)$ There is not enough information to determine whether the series converges or diverges.