In this video I go over further into infinite series and sequences and this time summarize an 8-step strategy for testing any given series for convergence or divergence. The strategy is not to be followed in order as that would be time consuming but rather to compare the type of series being dealt with the steps in the strategy. Since in my earlier videos I went over alternating series, geometric series, p-series, absolute series, and series with factorials or incrementally increasing powers (i.e. to the power of n), this video serves as a good summary and game plan for deciding how to go about tackling each type of series being presented. I also over 6 quick examples illustrating which test to perform.
The topics and their timestamps in the video are listed below:
1. @ 0:52 - Strategy for Testing Series
- @ 1:32 - Step 1: P-Series.
- @ 2:14 - Step 2: Geometric Series
- @ 3:19 - Step 3: Comparison Tests
- @ 7:32 - Step 4: Test for Divergence
- @ 8:18 - Step 5: Alternating Series Test
- @ 10:25 - Step 6: Ratio Test
- @ 16:00 - Step 7: Root Test
- @ 16:48 - Step 8: The Integral Test
2. Examples
- @ 18:40 - Example 1: Test for Divergence
- @ 20:34 - Example 2: Limit Comparison Test
- @ 23:16 - Example 3: The Integral Test (or Ratio Test)
- @ 26:54 - Example 4: Alternating Series Test
- @ 27:20 - Example 5: Ratio Test
- @ 28:38 - Example 6: Comparison Test
Download Video Notes: https://1drv.ms/b/s!As32ynv0LoaIh_YMrfZ1-cLDGKPt7Q?e=Q56IeX
View video notes on the Hive blockchain: https://peakd.com/mathematics/@mes/infinite-sequences-and-series-strategy-for-testing-series
Related Videos:
Sequences and Series Playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0EXHAJ3vRg0T_kKEyPah1Lz
Infinite Sequences: Limits, Squeeze Theorem, Fibonacci Sequence & Golden Ratio + MORE: https://peakd.com/mathematics/@mes/infinite-sequences-limits-squeeze-theorem-fibonacci-sequence-and-golden-ratio-more
Infinite Series: Definition, Examples, Geometric Series, Harmonics Series, Telescoping Sum + MORE: https://peakd.com/mathematics/@mes/infinite-series-definition-examples-geometric-series-harmonics-series-telescoping-sum-more
Infinite Sequences and Series: The Integral Test and Estimate of Sums: https://peakd.com/mathematics/@mes/infinite-sequences-and-series-the-integral-test-and-estimate-of-sums
Infinite Sequences and Series: The Comparison Tests: https://peakd.com/mathematics/@mes/infinite-sequences-and-series-the-comparison-tests
Infinite Sequences and Series: Alternating Tests: https://peakd.com/mathematics/@mes/infinite-sequences-and-series-alternating-tests
Infinite Sequences and Series: Absolute Convergence and the Ratio/Root Tests: https://peakd.com/mathematics/@mes/infinite-sequences-and-series-absolute-convergence-and-the-ratio-root-tests .
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