Lesson Preview
In this lesson we'll introduce series (Module 1) and begin the journey of discussing their convergence (Module 2). We'll see that series are intimately linked to sequences, and thus that the convergence of a series can be reduced to the convergence of an associated sequence called the sequence of partial sums. This link will give us one answer to this Unit's driving question: Does an infinite sum have a sum? But it will also reveal limitations to using the convergence of the sequence of partial sums to determine the convergence of a series. That will then prompt us to search for alternative methods to determine whether a series converges, which will occupy the next few lessons.
The lesson notes below contain a learning plan with three stages -- Learn, Reflect, and Practice -- and guidance for what to do within each stage. Some tips for you as you work through this resource, and those that it points to:
I recommend using Cornell Notes (or a modification of it; see this video starting at the 1:05 mark) to take notes on the lesson and the videos. This note-taking method balances detail with big-picture thinking to help you summarize and retain what you are learning. See this other video for additional note-taking techniques you might want to experiment with.
If you are currently enrolled in this course with me, submit the written reflections Google Form I have emailed you after working through the lesson notes and videos. Some tips:
Submit substantive, but concise, answers to each question; you will be doing the future you a big favor by taking time now to accurately and succinctly summarize what you have learned from the lesson.
Send yourself a copy of your reflections; they will come in handy later when you start preparing for quizzes and other assessments.
If you are not currently enrolled in this course with me, those written reflections ask three reflective questions designed to help you retain what you've learned and pinpoint any remaining areas of confusion. Those questions are:
Please summarize the main mathematical takeaways from the lesson notes.
What was the most interesting part of what you learned, and why?
What, if anything, do you still find confusing?
Work through the practice problems suggested below to see how much of this lesson you've understood.