Sequences 2 - Examples of Convergent/Monotonic/Bounded

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Calculus: For the following sequences, we consider (a) convergence/divergence, (b) monotonic increasing/decreasing, and (c) boundedness. (I) a_n = cos(n pi),
(II) a_n = cos(n pi)/n^2, (III) a_n = ln(n^{3/2})/n^{3/2}.

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This is a good trick to know. On even multiples of pi, cosine is always = 1; on odd multiples, cosine is always = -1. Note that the exponent n matches the signs up perfectly. Hope that helps!

MathDoctorBob
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All of the videos are awesome! You make the material easy to understand. Thanks much!

TheLiz
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very nice vid Dr. Bob, definitely some competition for patrickJMT.

baumboards
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@surefiretj14 You're welcome, and thanks for the support. The hardest part for me is the production, but it improves as I learn more about my tools. - Bob

MathDoctorBob
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@TheLiz217217 You're welcome, and thanks again for the feedback! - Bob

MathDoctorBob
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@baumboards Thanks for the comment. There's room for everyone here, so it is win-win for the students. I'm grateful to have a global classroom. (No love for Khan? He gets props for being first.) - Bob

MathDoctorBob
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If I wanted to be a real math nerd, a pun on "littoral" would be appropriate here in a few senses, but I don't roll like that.

MathDoctorBob
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