Mathematics-I for B.Sc. CSIT First Semester, TU - Alternating Series and Leibniz Test

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Kshitiz Mangal Bajracharya

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Published on May 22, 2023 6:10:55 PM ● Video Link: https://www.youtube.com/watch?v=pk04-iopKD0

Duration: 1:48:53

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00:00 Definition of Alternating Series and some brief discussions

02:23 Absolute Convergence Test for Alternating Series

04:27 Example where Absolute Convergence Test works
06:23 Example where Absolute Convergence Test fails

09:05 Leibniz Test for Alternating Series

14:16 Example 1 to illustrate Leibniz Test
35:37 Example 2 to illustrate Leibniz Test
41:51 Example 3 to illustrate Leibniz Test

47:31 Example of divergent alternating series (Leibniz Test isn't applicable)

51:29 Example 4 to illustrate Leibniz Test
54:16 Example 5 to illustrate Leibniz Test
58:52 Example 6 to illustrate Leibniz Test
1:03:16 Example 7 to illustrate Leibniz Test
1:08:23 Example 8 to illustrate Leibniz Test

1:12:21 Example 1 to show what to do if we are to test only the convergence of alternating series
1:17:29 Example 2 to show what to do if we are to test the absolute and conditional convergence of alternating series

1:24:59 A summary on what to do if we want to test convergence vs what to do if we want to test absolute and conditional convergence

1:30:59 Example 2 to show what to do if we are to test only the convergence of alternating series
1:34:20 Example 3 to show what to do if we are to test only the convergence of alternating series
1:36:21 Example 4 to show what to do if we are to test only the convergence of alternating series

1:39:37 Example 2 to show what to do if we are to test the absolute and conditional convergence of alternating series