Infinite Sequences and Series: Alternating Tests

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    mes

    Published on Jun 22, 2020
    About :

    In this video I go over further into the wonderful world of Infinite Sequences and Series and this time look at Alternating Series; which are series that alternate from positive and negative terms. When dealing with alternating positive and negative terms it is important to develop specific theorems and methodologies in order to better analyze whether they converge or diverge. Often times it is best to view the odd and even terms of the series separately since they would have the same signs when grouped together. I go over this and much more throughout the video so make sure to follow along!

    The topics and their timestamps in the video are listed below:

    1. @ 1:28 - Introduction to Alternating Series
    2. @ 6:06 - The Alternating Series Test
      • @ 14:00 - Proof of the Alternating Series Test
      • @ 27:50 - Example 1
      • @ 32:03 - Example 2
      • @ 36:28 - Example 3
    3. @ 53:43 - Estimating Sums
      • @ 55:05 - Alternating Series Estimation Theorem
      • @ 59:27 - Example 4
      • @ 1:11:26 - Important Note
    4. Exercises
      • @ 1:11:52 - Exercise 1
      • @ 1:48:22 - Exercise 2
        • @ 2:08:50 - Proof of the Multiplication Rule for Logarithms
      • @2:14:05 - Exercise 3

    Download Video Notes: https://1drv.ms/b/s!As32ynv0LoaIh_IqKIuB648PDvj1bQ?e=zqe5ZE

    View video notes on the Hive blockchain: https://peakd.com/mathematics/@mes/infinite-sequences-and-series-alternating-tests

    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 .


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