Question $12$

$10$ pts

Determine whether the series ${\displaystyle \underset{n=2}{\overset{}{}}}\frac{(-1{)}^n}{nln7n}$ converges conditionally or absolutely$,$ or diverges.

Your paperwork is what will be scored for this problem. This may cause your score to drastically increase or drastically decrease upon grading. On your paperwork, be sure to state what Test of Convergence applied $(1$ point$),$ apply the test correctly, showing all steps, $(4$ points$),$ draw an appropriate conclusion $(2$ points$),$ state and apply any other Test of Convergence, as necessary, $(2$ points$),$ and draw final conclusion $(2$ points$).$

The series converges absolutely$.$

The series diverges.

The series converges absolutely but does not converge conditionally.

The series converges conditionally but does not converge absolutely$.$