In this video I explore further into Infinite Sequences and Series and this time consider series that have involve the absolute values of a sequence. This involves the concept of “absolute convergence” which I show that it implies convergence in general; although the reverse is not always the case. In this case, the very interesting concept of “conditional convergence” arises which allows for the convergence of a series simply by re-arranging the terms such that the positive and negative terms cancel out; which is only possible if a series is not absolutely convergent. I also go over two specific tests to determine absolute convergence and they are the ratio and root test which are as their names describe. Half of this video is spent on 4 exercises at the end of the video and are a great way to reinforce the concepts introduced in this video.
The topics and their timestamps in the video are listed below:
Please note the following list of corrections which I realized during the making of the video:
Download Video Notes: https://1drv.ms/b/s!As32ynv0LoaIh_NXBMhbCTS1dvztYg?e=EZPQ9u
View video notes on the Hive blockchain: https://peakd.com/mathematics/@mes/infinite-sequences-and-series-absolute-convergence-and-the-ratio-root-tests
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 .
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