Consider the following series.

${\displaystyle \underset{n=2}{\overset{}{}}}\frac{(-1{)}^n}{ln(6n)}$

Test the series for convergence or divergence using the Alternating Series Test.

Identify ${}_N.$

Evaluate the following limit$.$

$\underset{n}{lim}{b}_n$

Since $\underset{n}{lim}{b}_{n}0$ and $b_{n1}{}_n$ for all $n$

Test the series ${\displaystyle \underset{?}{\overset{?}{}}}{b}_n$ for corverpence or divergence using an appropriate Comparison Test.

The series converges by the Direct Comparison Test. Each term is less than that of a divergent geometric series.

The series diverges by the Direct Comparison Test. Each term is greater than that of a comparable harmonic serles.

The series diverges by the Limit Comparison Test with a divergent peometric series.

The series converges by the Limit Comparison Test with a convergent p$-$series.

Determine whether the given alternating series is absolutely corvergent, conditionally convergent, or divergent.

absolutely convergent

conditionally cohverpent

diverpent