Review Question 5: Recap on Tests for Convergence or Divergence of Infinite Series

1

  • 386
  • 0
  • 2.262
  • Reply

  • Open in the desktop app ADD TO PLAYLIST

    mes

    Published on Nov 15, 2023
    About :

    In this video I recap on 7 different types of tests for determining if an infinite series converges or diverges. The first is the Test for Divergence which states that if the limit of the sequence of terms does not approach 0, then the series is divergent. The second is the Integral Test, which states that the series is only convergent if its corresponding integral is also convergent. The third is the Comparison Test, which states that a series is convergent if every term of its sequence is smaller than that of a known convergent series. The fourth is the Limit Comparison Test, which states that if the limit of the ratio of the terms of 2 sequences is equal to a finite number c that is greater than 0, then either both series converge or both diverge. The fifth is the Alternating Series Test, which states that if the absolute value of all the terms of an alternating series is less than each subsequent term, and their limit approaches 0, then the alternating series is convergent. The sixth is the Ratio Test, which states that if the limit of the absolute value of the ratio of the n + 1 term divided by the n-th term is equal to a finite number less than 1, then the series is convergent. The seventh test is the Root Test, which states that if the n-th root of the absolute value of the n-th term is equal to a finite number less than 1, then the series is convergent.

    Note that for all the tests listed, they have similar conditions for when the series is divergent, or in the case of the Ratio and Root Tests, where the tests are inconclusive when the limits equal to 1.

    The timestamps of key parts of the video are listed below:

    • Question 5: 0:00
    • (a) Test for Divergence: 0:22
    • (b) Integral Test: 1:25
    • (c) Comparison Test: 3:32
    • (d) Limit Comparison Test: 4:43
    • (e) Alternating Series Test: 5:28
    • (f) Ratio Test: 8:01
    • (h) Root Test: 9:23

    This video was taken from my earlier video listed below:

    Related Videos:

    Sequences and Series playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0FjJpwnxwdrOR7L8Ul8VZoZ .


    SUBSCRIBE via EMAIL: https://mes.fm/subscribe

    DONATE! ʕ •ᴥ•ʔ https://mes.fm/donate

    Like, Subscribe, Favorite, and Comment Below!

    Follow us on:

    MES Truth: https://mes.fm/truth
    Official Website: https://MES.fm
    Hive: https://peakd.com/@mes

    MORE Links: https://linktr.ee/matheasy

    Email me: contact@mes.fm

    Free Calculators: https://mes.fm/calculators

    BMI Calculator: https://bmicalculator.mes.fm
    Grade Calculator: https://gradecalculator.mes.fm
    Mortgage Calculator: https://mortgagecalculator.mes.fm
    Percentage Calculator: https://percentagecalculator.mes.fm

    Free Online Tools: https://mes.fm/tools

    iPhone and Android Apps: https://mes.fm/mobile-apps

    Tags :

    math calculus science stemgeeks stemsocial palnet proofofbrain chessbrothers stem mathematics

    Woo! This creator can upvote comments using 3speak's stake today because they are a top performing creator! Leave a quality comment relating to their content and you could receive an upvote worth at least a dollar.

    Their limit for today is $0!
    Comments:
    Time until mes can give away $0 to their commenters.
    0 Days 0 Hours 0 Minutes 0 Seconds
    Reply:

    To comment on this video please connect a HIVE account to your profile: Connect HIVE Account

    17:15
    mes
    3 views a year ago $

    More Videos

    01:41
    26 views 3 years ago $
    03:34
    18 views a year ago $
    01:01
    1 views 4 years ago $