Calc 2, 24B, Geometric Series, Limit Comparison Test, Ratio Test, Alternating Series, 'Prove' 0=1

Calculus 2, Lecture 24B.

(0:00) Reminder that notation used was flexible...it's the idea that's important.
(0:28) Review geometric series.
(3:12) Example on Mathematica.
(4:40) Limit comparison test example and proof.
(10:44) Ratio test idea.
(13:30) Use the Ratio Test for an example whose terms are the ratio of an exponential function to a factorial.
(18:01) The Ratio Test gives no conclusion for p-series (when p is positive).
(18:46) Use the Alternating Series Test to conclude that alternating harmonic series converges.
(22:02) Faulty "proof" that 0 equals 1 ("prove" 0=1).