The screencast of the 2009-10 edition of How do we do proofs? (Part II) is now available from
http://wirksworthii.nottingham.ac.uk/webcast/maths/G12MAN-09-10/How-Proofs-II-0910/
Here some background knowledge of convergence of series is assumed. There is an associated handout available at
http://www.maths.nott.ac.uk/personal/jff/Teaching/Standard-Series.pdf
with some relevant background material, including some standard series and a bit about the comparison test.
Joel Feinstein
This screencast is now also available on YouTube in the Nottingham University maths playlist, http://www.youtube.com/user/NottmUniversity#g/c/A9721D7E1FB7CD34
or directly at
http://www.youtube.com/user/NottmUniversity#p/c/A9721D7E1FB7CD34/3/1l9gCIYmKd8
It may be easier to browse the maths playlist using the YouTube search:
http://www.youtube.com/view_play_list?p=A9721D7E1FB7CD34&sort_field=added