What is the best way to learn sequences/series?

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Discussion Overview

The discussion centers on strategies for mastering sequences and series in Calculus II. Participants share their experiences and suggest resources, techniques, and approaches to better understand the topic, which includes various convergence tests and their applications.

Discussion Character

  • Homework-related
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • One participant expresses difficulty in grasping sequences and series, particularly in applying different convergence tests like the Integral Test and Comparison Test.
  • Another participant suggests that doing numerous examples and obtaining a personal tutor could be beneficial.
  • Resources such as PatrickJMT and Khan Academy are recommended by one participant for additional learning materials.
  • A participant emphasizes the importance of understanding the theorems related to convergence tests, noting that each theorem outlines specific conditions for application.
  • One participant mentions that sequences and series differ from traditional calculus techniques and highlights the necessity of numerical analysis for solving more complex problems encountered in higher-level courses.
  • There is a suggestion to understand how functions can be represented by series, indicating a conceptual approach to the topic.

Areas of Agreement / Disagreement

Participants generally agree on the importance of practice and the use of resources, but there is no consensus on a singular best method or approach to mastering sequences and series.

Contextual Notes

Some participants note that the application of convergence tests requires careful attention to the conditions outlined in theorems, which may not be fully understood by all learners. Additionally, the transition from traditional calculus to sequences and series may introduce challenges that are not present in earlier topics.

Who May Find This Useful

This discussion may be useful for students struggling with sequences and series in calculus courses, as well as those seeking additional resources and strategies for mastering these concepts.

chans
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I've been doing alright in Calculus II but I can't seem to grasp sequences/series. The different tests like Integral Test, Comparison Test, Ratio/Root Tests also confused me in terms of how to apply them and when to apply them.

What is the best way for me to master this material? Any good sites or tutorials or basic strategies? For integration I learned it well by practicing integrating different integrals with different techniques, but when I try doing it for series/sequences I get stuck and can't retain the concepts.
 
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Same as for anything: do lots of examples - and get a personal tutor.
 
2 people I always recommend.
Www.patrickjmt.com
http://www.khanacademy.org/math/calculus/sequences_series_approx_calc

It also helps to play around with things like the Cantor set for fun and to familiarize yourself with the techniques used.
 
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chans said:
I've been doing alright in Calculus II but I can't seem to grasp sequences/series. The different tests like Integral Test, Comparison Test, Ratio/Root Tests also confused me in terms of how to apply them and when to apply them.
This should not confuse you if you pay close attention to the theorems where these rules are presented. Each theorem gives the conditions that must be in place to use the theorem, and what you can conclude when you apply the theorem to your series.


chans said:
What is the best way for me to master this material? Any good sites or tutorials or basic strategies? For integration I learned it well by practicing integrating different integrals with different techniques, but when I try doing it for series/sequences I get stuck and can't retain the concepts.
 
Do a lot of problems. It is just different from the other calculus stuffs. But as you go higher, there are more and more problems that cannot be solved by traditional integration or differentiations. It often need to be solved by numerical analysis, which is like series and sequence. You are going to encounter much more in Differential Equation and partial differential equation classes. All the Bessels, Legendre etc. are series.

Understand how the function being replaced by series, but after than, it is really a series that sum power of a variable together. That's the reason they called it numerical analysis!
 

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