I wrote up a summary of the various tests for convergence/divergence of infinite series that we discussed from Sections 10.2 and 10.3 of the text. You can use this as a reference as you do exercises, but also look at the examples in the textbook and the examples we did in class for each test:
https://openlab.citytech.cuny.edu/?get_group_doc=15883/1430748441-Math1575-InfiniteSeriesTests.pdf
UPDATE: I have extended the document to include the Alternating Series Test (Section 10.4) and the Ratio Test (Section 10.5). You can download the new version of the document here:
The trickiest of these is probably the limit comparison tests. It may be helpful to look at some video examples:
