Monotonic Sequences and Bounded Sequences - Calculus 2 Video
This calculus 2 video tutorial provides a basic introduction into monotonic sequences and bounded sequences. A monotonic sequence is a sequence that is always increasing or decreasing. You can prove that a sequence is always increasing by showing that the next term is greater than the previous term. This video also discusses bounded sequences. A sequence can be bounded above or have an upper bound it it has a maximum value it can reach. If there is a minimum value in the sequence, then it has a lower bound or it's bounded below. A sequence that is bounded above and bounded below is said to be bounded. A monotonic sequence that is bounded is said to be convergent. This video explains how to determine the convergence and divergence of a sequence by determining if its a monotonic sequence and if its a bounded sequence.
Improper Integrals:
https://www.youtube.com/watch?v=ND9cEdfCFr0
Converging & Diverging Sequences:
https://www.youtube.com/watch?v=XdkoTb8PEG0
Monotonic & Bounded Sequences:
https://www.youtube.com/watch?v=tHy3TXmZpF0
Absolute Value Theorem - Sequences:
https://www.youtube.com/watch?v=kH5Zqg5j-3M
Squeeze Theorem - Sequences:
https://www.youtube.com/watch?v=21loY9MBK3A
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Geometric Series & Sequences:
https://www.youtube.com/watch?v=zRKZ0-kOUZM
Introduction to Series - Convergence:
https://www.youtube.com/watch?v=zg9N2gAf6a4
Divergence Test For Series:
https://www.youtube.com/watch?v=nC_IU1IzzS4
Harmonic Series:
https://www.youtube.com/watch?v=OqBZCycIYfw
Telescoping Series:
https://www.youtube.com/watch?v=XVkdhU6nJbo
__________________________________
Integral Test For Divergence:
https://www.youtube.com/watch?v=f9SJz4-UaQQ
Remainder Estimate - Integral Test:
https://www.youtube.com/watch?v=vaU5DDcTfZk
P-Series:
https://www.youtube.com/watch?v=x621rtIwb_4
Direct Comparison Test:
https://www.youtube.com/watch?v=oZtAgihok5s
Limit Comparison Test:
https://www.youtube.com/watch?v=LBxYQ0TJxYM
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Calculus Final Exam and Video Playlists:
https://www.video-tutor.net/
Full-Length Videos and Worksheets:
https://www.patreon.com/MathScienceTutor/collections
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