Please see the images below to be able to construct a solution to a problem that requires "Test for Divergence" (also known as "Divergence Test") using the action "Series: Divergence Test":
- After selecting the series (left click), type "Diver..." into the "Actions" search box then select "Series: Divergence Test"
- In the additional window, compute the limit to see if the limit of the general term is not equal to zero or it does not exist and in this example the limit exists but it is not equal to zero, which implies the series is divergent by "Test for Divergence".
- Hit "Done" . Finally select the right answer and click on "Check my answer" to see your score.
Note that you can also apply the "Test for divergence" without the action.
Please see the images below to be able to structure a solution without the action:
- Select only the general term in the sum and replace "k" by "x" (note that you do not have to do this if the limit did not require L'Hospitals rule).
- Then take the limit as x goes to infinity
- Compute the limit
- This also implies that limit of the general term of the series is also 1 and so by "Test for divergence" we can conclude that the series is divergent.
