Monotonic Sequences and Bounded Sequences - Calculus 2

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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:


Converging & Diverging Sequences:


Monotonic & Bounded Sequences:


Absolute Value Theorem - Sequences:


Squeeze Theorem - Sequences:


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Geometric Series & Sequences:


Introduction to Series - Convergence:


Divergence Test For Series:


Harmonic Series:


Telescoping Series:


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Integral Test For Divergence:


Remainder Estimate - Integral Test:


P-Series:


Direct Comparison Test:


Limit Comparison Test:


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