The main purpose of our study of series and sequences is to understand power series. Here is a set of practice problems to accompany the series and sequences chapter of the notes for paul dawkins calculus ii course at lamar university. Sequences and series a to every series, there are two associated sequences. Ii the ratio test cannot be used to determine whether. Nov 22, 2015 calculus 2 geometric series, p series, ratio test, root test, alternating series, integral test duration.
All of the topics are covered in detail in our online calculus 2 course. Study techniques infinite series table indepth practice 100 problems exam preparation calculus practice exams infinite series exam a infinite series exam b. Problem 3 find the volume of the solid generated by. Here are a set of practice problems for the series and sequences chapter of the calculus ii notes.
Math 222 calculus ii practice test 3 sequences and series. Also, the conditions referred to in number 27 are the hypotheses of the integral test, namely that fx must be continuous, positive, and decreasing. Since the limit is less than 1, the root test says that the series converges absolutely. Friday, may 2, 8 am in fh 2100 solutions to quizzes. For each of the following series, determine whether it converges or diverges. Khan academy is a nonprofit with the mission of providing a free, worldclass education for anyone, anywhere. Review problems for a calculus 2 exam that covers series. Math 0230 calculus ii angela athanas 422 thackeray hall office hours spring 20. Integration techniques, sequences and series, convergence tests, taylor series, parametric and polar curves. Final exam, part 2 in class student learning outcomeslearning objectives learning objectives for math 2414, calculus ii. Problem 2 evaluate the following integrals r x5 cosx3dx solution. These are the ones you will come across the most in calculus. Example of a series that converges but does not converge absolutely. The term test can be used to show that the following series dont converge.
Sep 17, 2018 youre about to embark on the thrilling adventure known as calculus 2. Practice exam 2 exam 2 here is a copy of a first exam for practice. C or better in 1151, 1156, 152, or 161, or in 114 or 1114. The root test also does not apply in this scenario. Review problems for sequences and series note that in number 28, there may be more than one statement that is false. We can now return to the example from the previous page and a similar example. Series and sequences in this chapter we introduce sequences and series.
Does this sequence converge and, if it does, to what limit. Calculus ii will cover sections 5, 6, 7, and 8 of the textbook, starting with section 5. A geometric series x1 n0 arn converges when its ratio rlies in the interval 1. If the answer is \no, give a counterexample that is, give an example of a series x1 n1 a n such that lim n. However, if you are pressed for time, this video will give you plenty. Not open to students with credit for any higher numbered math class. However, in the realm of infinity, unusual things start to happen. Learn calculus 2 series with free interactive flashcards. If a certain topic is unclear one should look for similar problems in the textbook for further practice. A power series is like a polynomial of in nite degree. You may use a graphing calculator that does not have symbolic manipulation capabilities. We discuss whether a sequence converges or diverges, is increasing or decreasing, or if the sequence is bounded. Thomas calculus, 12th edition, by thomashassweir course description presents a continuing study of integration techniques, applications to physics and engineering, improper integrals, transcendental functions, first order differential equations, series and sequences, parametric equations and polar coordinates.
If youd like a pdf document containing the solutions the download tab above contains links to pdfs containing the solutions for the full book, chapter and section. We will then define just what an infinite series is and discuss many of the basic concepts involved with series. Sections covered from calculus 8th edition by james stewart. Calculus 2 geometric series, pseries, ratio test, root test, alternating series, integral test duration. However, because of the \\left 1 \rightn 2 \ we cant compute this limit using our knowledge of computing limits from calculus i. Sequences may be written in several different ways. Note as well that there really isnt one set of guidelines that will always work and so you always need to be flexible in following this set of guidelines. This is not the best way to learn infinite series and ace your exam. A summary of all the various tests, as well as conditions that must be met to use. Power series, their interval of convergence and their applications. The question usually asks students to write a taylor or maclaurin series and to answer questions about it and its interval of convergence, or about a related series found by differentiating or integrating. First of all, the two terms, sequence and series, are not interchangeable. Introduction to series and sequences math 121 calculus ii.
I have neither given nor received aid on this exam. The last bc question on the exams usually concerns sequences and series. Topics include alternating series test, ratio test, root test, absolute convergence, conditional convergence, taylor polynomials, and. The following video provides an outline of all the topics you would expect to see in a typical singlevariable calculus 2 class i. Show step 2 recall however, that we had a nice fact in the notes from this section that had us computing not the limit above but instead computing the limit of the absolute value of the sequence terms. We have built a page around that video with each problem stated for you and a video clip with the solution. If you enroll prior to that date, youll be able to access the course through september 2018. For students on campus, its all about the comfo for those bates students still on campus, its not remotely the same, but familiar foods and faces from dining services do help. The course emphasizes not just getting answers, but asking the question why is this true. In this section we give a general set of guidelines for determining which test to use in determining if an infinite series will converge or diverge.
Enrollment for this course will close permanently on march 30, 2018. Infinite series is an unusual calculus topic but series can be very useful for computation and problem solving, especially when it comes to integration and differential equations. The topics may appear in other freeresponse questions and in multiplechoice. This course is devoted to the study of elementary transcendental functions, techniques and applications of integration, sequences, series, power series with applications, parametric equations, and polar coordinates. Learn vocabulary, terms, and more with flashcards, games, and other study tools. The nth term test and the divergent test may not be used to determine whether this series converges, since this is a special case. Find the common difference or the common ratio and write the equation for the nth term. The sample tests are just to give you an idea of the a general idea of the topics covered, the level of difficulty, how questions may be worded and, if solutions are provided, what is the acceptable level of detail required in the solutions. Sequences and series is an introduction to sequences, infinite series, convergence tests, and taylor series. Calculus 2 geometric series, pseries, ratio test, root test. Series convergence tests math 121 calculus ii spring 2015 some series converge, some diverge.
Introduction to series and sequences math 121 calculus ii d joyce, spring 20 the goal. Level up on the above skills and collect up to 800 mastery points. Choose your answers to the questions and click next to see the next set of questions. Infinite series sequences basic properties divergence. We know when a geometric series converges and what it converges to. Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more. Youre about to embark on the thrilling adventure known as calculus 2. Choose from 500 different sets of calculus 2 series flashcards on quizlet.
To view the acrobat pdf files for each document, click on the symbol. From your previous studies, you have understood how calculus describes the rate of change and how we use limits and derivatives to help define and represent that change. Does the series described by a n 1n n2 2n2 5 converge. Now that weve got all of our tests out of the way its time to think about organizing all of them into a general set of guidelines to help us determine the convergence of a series. Use the following formula, where is the first term of the series, and is the ratio that must be less than 1. We will illustrate how partial sums are used to determine if an infinite series converges or diverges. Limits derivatives integrals infinite series parametric equations conics polar coordinates laplace transforms. A summary of all the various tests, as well as conditions that must be met to use them.
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