Lecture 12: The Ratio, Root, and Alternating Series Tests

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MIT 18.100A Real Analysis, Fall 2020
Instructor: Dr. Casey Rodriguez

We show three important tests for convergence of infinite series: the ratio, root, and alternating series tests.

License: Creative Commons BY-NC-SA

  1. MIT OpenCourseWare
  2. Ratio test
  3. alternating series test
  4. infinite series
  5. root test
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Комментарии
Автор

So, I guess this marks the end of:
Single Variable analysis: Sequences and Series.
As always, I praise MIT OCW and similar programs for this free information.

So far, it's been great. Although the proofs kinda beat me, it is reeally nice to see the proofs of the theorems you wouldn't see in your classic calculus class. (Yes, this implies that I haven't even taken Calculus formally yet.)

Since I try to understand the proofs uniquely to grasp a better understanding of usual Calculus, I've been mostly focused on applications exercises more than proofs, but trust me, I've understood mostly everything so far, in a kind of ordered way, somehting like this:

Understanding Calculus ≤ Understanding of analysis for calculus ≤ Understanding of analysis

We take the limit as Understanding goes to infinity, then :

L ≤ Understanding of analysis for Calculus ≤ U
(Asuming the others converge, by squeeze theorem)
and therefore: there exists a B≥0 s.t |Understanding(analysis, calculus)|≤B (converges <=> bounded)

*This does not make ANY sense, its just fun rambling and its probably wrong anyway.

Javy_Chand
Автор

at 34'40, limsupXn should be >1 instead of >= 1 right?

HaozheJiang