周次: 14 日期: May 27, 2022 节次: 2 In this lecture, we will continue the discussion of absolute and conditional convergence, give the absolute convergence test to show any absolutely convergent series itself must converge. We also look at the difference between absolute and conditional convergences by showing that an absolute convergent series remains the same even after the rearrangement of the terms. However,...

周次: 14 日期: May 25, 2022 节次: 1 In this lecture, we continue the discussion on the root test (for the series with non-negative terms). And we discuss alternating series, there’s a test called Leibniz’s or alternating series test. Alternating series converges in a manner that positive and negative terms...

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,...