Sequences and Convergence
Welcome to Week 9.
We will finish working on Chapter 2 this week.
Here is a video lecture with some advice on the Chapter 2 exam question.
Slides from Lecture 17 on Chapter 2 exam advice, annotated.
We will start our work on Chapter 3 with Wednesday’s lecture. The theme is convergence of sequences and series. We have already seen that an irrational number (for example) can be the limit of a sequence of rational numbers, we can think of π for instance as the limit of its successive decimal approximations. In this chapter we will give a precise meaning to the concept of convergence of a sequence, and use it to consider the question of whether the sum of infinitely many numbers can ever have a numerial value, and even whether a function can be represented as an infinite sum. Answers to these questions have very important applications to practical problems of approximating quantities that cannot be computed precisely, and even for determining values of everyday functions like the trigonometric ones.
Here is (last year’s version of) Lecture 18.
Slides for Lecture 18, without annotation, and annotated.