If you are required to take only one semester of calculus course, go for our college calculus rl411. We can now return to the example from the previous page and a similar example. Selection file type icon file name description size revision time user. Page 838 sigma notation college algebra wednesday april 5. There is online information on the following courses. Gonzalezzugasti, university of massachusetts lowell 1. Definition, with examples of convergent and divergent sequences. Thus, the first term corresponds to n 1, the second to n 2, and so on. Convergence of a sequence, monotone sequences in less formal terms, a sequence is a set with an order in the sense that there is a rst element, second element and so on. Review sheet for calculus 2 sequences and series sequences convergence a sequence fa ngconverges if lima n exists and is nite.
The sum of an infinite geometric series is 9 and its common ratio is 3 1. Our calculus volume 3 textbook adheres to the scope and sequence of most general calculus courses nationwide. Catalog description math 143 calculus iii 4 units ge area b1 prerequisite. The sequence we saw in the previous paragraph is an example of whats called an arithmetic sequence.
Limits of ratios an important concern of calculus is what happens to the ratio. Infinite sequences and series, vector algebra, curves. Sequences and power series kenyatta university library. This text comprises a threetext series on calculus. And this sort of thinking is needed to make sense of numbers like. Introduction to series and sequences math 121 calculus ii. Notes on infinite sequences and series 7 1 12 1 3 14 y1x 0 0. Series are similar to sequences, except they add terms instead of listing them as separate elements. The first part covers material taught in many calc 1 courses. A power series is like a polynomial of in nite degree.
For the love of physics walter lewin may 16, 2011 duration. This sequence of three courses cover the single variable and multivariable calculus. Find the nth term rule of sequence of each sequence, and use it to determine whether or not the sequence converges. The range of the function is still allowed to be the real numbers. Calculus 3, introduction to sequences and series youtube. Powered by create your own unique website with customizable templates. If you are required to take three semesters of calculus courses. Series recall that a series, roughly speaking, is the sum of a sequence. Questions and commands are never propositions, but statements like \my buick is maroon t and \my buick is black f are propositions. Here are a set of practice problems for the series and sequences chapter of the calculus ii notes. Stewart calculus 7e solutions chapter 11 infinite sequences and series exercise 11. Lets discuss these ways of defining sequences in more detail, and take a look at some examples. A sequence is a function with domain the natural numbers n1,2, 3, or the nonnegative integers, z.
These simple innovations uncover a world of fascinating functions and behavior. The main purpose of our study of series and sequences is to understand power series. The point in question is the vertex opposite to the origin. Other useful facts a n converges to zero if and only if ja njalso converges to zero.
A sequence is converging if its terms approach a specific value as we progress through them to infinity. The terms of a sequence may be arbitrary, or they may be defined by a formula, such as s n 2n in general, n starts at 1 for sequences, but there are times when it is convenient for n to start at 0, in. Represent and calculate sums of series with sigma notation. Remember that we are assuming the index n starts at 1. In the sequel, we will consider only sequences of real numbers. The sum of an infinite series is three times its first term. Sequences and series notes for math 3100 at the university. Calculus 2 geometric series, pseries, ratio test, root test, alternating series, integral test duration. Volume 3 covers parametric equations and polar coordinates, vectors, functions of several variables, multiple integration, and secondorder differential equations. Series, convergence, divergence mit opencourseware. In the end, all the key functions of calculus appear as infinite polynomials except the step function.
If youd like a pdf document containing the solutions the download tab above contains links to pdf s containing the solutions for the full book, chapter and section. Topics covered are three dimensional space, limits of functions of multiple variables, partial derivatives, directional derivatives, identifying relative and absolute extrema of functions of multiple variables, lagrange multipliers, double cartesian and polar coordinates and triple integrals. Applications of calculus 38 exercises 39 chapter 3. Chapter 2 limits of sequences university of illinois at.
A realvalued function with domain the natural numbers n f1,2 3. Sequences examples showing convergence or divergence. Deturck university of pennsylvania march 29, 2018 d. Sequences and series department of mathematics university of. Math 142 with a grade of c or better or consent of instructor.
Other functions will also be regarded as sequences. A read is counted each time someone views a publication summary such as the title, abstract, and list of authors, clicks on a figure, or views or downloads the fulltext. A sequence fa ngis called monotonic if it is either increasing or decreasing. Introduction to series and sequences math 121 calculus ii d joyce, spring 20 the goal.
Convergent and divergent sequences video khan academy. In this sequence, the pattern is that i started with a 1, and add 3 to get the next term. Here is a set of notes used by paul dawkins to teach his calculus iii course at lamar university. If a n b n for every n large enough, then the series x1 n1 a n and x1 n1 b n either both converge or both diverge. This is a summary of the main points weve dis cussed in class about the infinite sequences.
Sequences and series harvard mathematics department. This is correct, and will have significant value to us in this course. Calculus bc and bcd drill on sequences and series by susan e. Precalculus 11 chapter 1 sequences and series created by ms. In general, every text in the calculus series is given a number here 3 and a letter here b where a means compendium, b means guidelines for solutions. This sequence is different from the first two in the sense that it doesnt have a specific formula for each term. Squeeze theorem if b n a n c n for all values of n, and limb n limc n l, then it implies that lima n l. The second text covers material often taught in calc 2. Throughout calculus volume 3 you will find examples and exercises that present classical ideas and techniques as well as modern applications and methods. The geometric series 1 368 10 lnfinlte series 1 1 10. Derivations and explanations are based on years of classroom experience on the part of longtime calculus professors, striving for a balance of clarity and rigor that has proven successful with their.
135 796 1378 1194 709 1415 1166 1300 848 1348 543 72 1198 102 180 152 1350 6 576 798 1333 378 957 1186 1060 1337 1205 1160 424 215 1197 701 965 220 1347 478 289