Lesson 12.6 Absolute Convergence, Ratio & Root Tests

Calculus 2 Lesson 12.6 Absolute Convergence
The following topics are the most important. Typical exercises from Calculus, 5^th edition, by James Stewart, are assigned at the end of each objective. In smaller print following the objective is a guide for the reading assignment in the form of page numbers in the text and notes regarding the reading about the objective.
1.		Define "absolute convergence" and "conditional convergence". Text P776&777
	P776	The definition of absolute convergence is given in box 1 on this page. The theorem in box 3 on the next page is a result that you need to know. Look at Example 1.
	P777	The definition of conditional convergence is given in box 2 on this page. Look at Example 2.
	P777	To conclude that a series is conditionally convergent, you must use two tests: one to show that the series is not absolutely convergent and another to show that the series is convergent.
2.		Determine whether a series is absolutely convergent, conditionally convergent or divergent using among other things,
2a.			the previous methods, P781#5,7,17
	P777		We use absolute convergence when the the terms do not alternate but some terms are positive and some are negative. Look at Example 3.
2b.			the ratio test, P781#1,3,9,15,31
	P778		The definition is given in the box at the top of this page. Look at Examples 4 and 5.
2c.			the root test. P782#23,24
	P780		The definition is given in the box in the middle of this page. Look at Example 6.
Maple Assignment: none