Series

周次: 13 日期: May 20, 2022 节次: 2 In this lecture, the Comparison Test is upgraded to the limit case. In addition, two new tests based on the comparison with respect to the geometric series is given. These are called the Ratio Test and the Root Test, respectively. Note that all the tests are designed for a series with non-negative terms. § 11.4 The...

周次: 13 日期: May 18, 2022 节次: 1 In this lecture, we develop some convergence tests for the series with non-negative terms. These are the Integral Test and Comparison Tests. Both tests are based on the Monotonic Bounded Theorem for partial sum sequences. Before developing the tests, we will recap the previous section first. I. Recap: § 11.2 Series Basic Problems for Series Primarily,...

周次: 12 日期: May 13, 2022 节次: 2 In this lecture, we will talk about series, we introduce the sigma notation, and utilize limit to define the sum of a series. Primarily, there are two types of series whose sums can be found directly, by definition. Those are called Geometric Series and Telescoping Series. To study a divergent series, we introduce the $n$th term...

周次: 12 备注: Attendance check 日期: May 11, 2022 节次: 1 In this lecture, we continue the discussion of infinite series. We introduce the L’Hôpital’s Rule to the limit finding problems, and conclude this section by an important type of convergent sequences, called bounded monotonic sequences. Then we will talk about series,...

周次: 11 日期: May 6, 2022 节次: 2 In this lecture, we will discuss series and sequences, these are new concept and very important ones. Before talking about series, we will talk about sequences. Overview In this chapter we study how to add together infinitely many numbers. This is a subject of the theory of infinite series. It is clear that infinite sum sometimes...

在数学分析中有很多习题是关于数项级数的收敛性的。也有很多关于收敛性的判别方法。在这些判别法中，对于一般项级数的判别方法，一般的教材中会介绍绝...