Answer like a calculus student in calc with analytical geometry and show all work Directions: Show all work. Proper notation is required to receive full credit.

Determine whether the following alternating series converges or diverges.

${\displaystyle \underset{n=1}{\overset{}{}}}\frac{(-1{)}^n}{n^3}$

Use the Alternating Series Test to determine the convergence of the series.

${\displaystyle \underset{n=1}{\overset{}{}}}\frac{(-1{)}^n}{\sqrt[\phantom{2}]{n}}$

Estimate the error when approximating the sum of the series by its first $5$ terms.

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