Sequences and series pdf

Lesson 123 infinite sequences and series 777 example 3. Sequences via lists the method of using a list to specify a sequence perhaps is the most tricky, since it requires us to look at a short piece of a sequence, and guess at the pattern or rule that is being used to produce the terms in the sequence. A sequence has the limit l and we write or if we can make the terms as close to l as we like by taking n sufficiently large. Intuitively, a sequence is an ordered list of objects or events. Series are similar to sequences, except they add terms instead of listing them as separate elements. Its just two different sets of equations, but if youve got them at your fingertips click on thumbnail to the right to see a pdf of all the formulas. The purpose of this chapter is to introduce a particular way of. Any finite series has a sum, but an infinite geometric series may or may not have a sum. Free pdf download of ncert solutions for class 11 maths chapter 9 sequences and series solved by expert teachers as per ncert cbse book guidelines. Arithmetic and geometricprogressions mctyapgp20091 this unit introduces sequences and series, and gives some simple examples of each. They dont include multivariable calculus or contain any problem sets.

The marginal propensity to consume mpc is defined as the percentage of a dollar by which consumption increases when income rises by a dollar. Arithmetic sequences and series algebra 2, sequences and. If r 1 the sequence converges to 1 since every term is 1, and likewise if r 0 the sequence converges to 0. To find a rule for s n, you can write s n in two different ways and add the results. As a function of q, this is the riemann zeta function. Leading to applying the properties of geometric sequences and series to functions that illustrate growth and decay 1 arithmetic sequence term of a sequence or series. Sequences and series are most useful when there is a formula for their terms. An infinite series is the formal sum of the terms of an infinite sequence. Introduction to series and sequences math 121 calculus ii d joyce, spring 20 the goal. Begin with one sheet of 11 by 17 paper and four sheets of notebook paper.

For help with downloading a wikipedia page as a pdf, see help. In progressions, we note that each term except the first progresses in a definite manner. When we use the phrase sum of a series, we will mean the number that results from adding the terms, the sum of the series is 16. We discuss whether a sequence converges or diverges, is increasing or decreasing, or if the sequence is bounded. The easiest way to get used to series notation is with an. Sequentially complete nonarchimedean ordered fields 36 9. All sequences and series exercise questions with solutions to help you to revise complete syllabus and score more marks. We will then define just what an infinite series is and discuss many of the basic concepts involved with series.

Chapter 6 sequences and series of real numbers we often use sequences and series of numbers without thinking about it. Ncert solutions for class 11 maths chapter 9 sequences and. Note that a series is the sum of a number of terms of a sequence. Reading and writingas you read and study the chapter, fill the journal with examples for each lesson. Introduction to series and sequences math 121 calculus ii. Exercises on these topics are on the following pages. Fibonacci numbers fibonacci numbers form an interesting sequence of numbers in which each element is obtained by adding two preceding elements and the sequence starts with 0 and 1. Review problems involving sequences and series pgs. Sequence and seriesdefinition, types, formulas and examples. The main purpose of our study of series and sequences is to understand power series. Thus, the first term corresponds to n 1, the second to n 2, and so on. This note covers the notions of convergence of sequences and series and the nature of the real numbers. A geometric series is the sum of the terms of a geometric sequence.

We will discuss if a series will converge or diverge, including many of the tests that can be used to determine if a. Ncert solutions for class 11 maths chapter 9 sequences and series. Find the common difference or the common ratio and write the equation for the nth term. For a given power series, there are only three posibilities. Miss mathematical induction sequences and series john j oconnor 200910. A guide to number patterns, sequences and series teaching approach this series covers revision of linear number patterns, introduction to quadratic sequences and finding the nth term. To continue the sequence, we look for the previous two terms and add them together.

Chapter 11 sequences and series 577 sequences and seriesmake this foldable to help you organize your notes. An arithmetic series is the sum of an arithmetic sequence. Represent the sum of a series, using sigma notation determine the sum of the first n terms of an arithmetic or geometric series pgs. Build a sequence of numbers in the following fashion. Determine what type of sequence the following are and then complete the problem. It also explores particular types of sequence known. A series can be finite for example, it might only have 25 terms or infinite, and the notation needs to allow for both. One of my favorites is sadly long out of printits w. Example 1 write the first three terms in each of the following sequences defined by the following. Notes on infinite sequences and series 7 1 12 14 y1x 0 0. In an arithmetic sequence the difference between one term and the next is a constant. Remember that we are assuming the index n starts at 1. Sequences and series this is a wikipedia book, a collection of wikipedia articles that can be easily saved, imported by an external electronic rendering service, and ordered as a printed book.

A sequence can be thought of as a list of numbers written in a definite order. A series of numbers is said to be in harmonic sequence if the reciprocals of all the elements of the sequence form an arithmetic sequence. Page 838 sigma notation college algebra wednesday april 5. 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. Solutions to the exercises in this booklet are available at the website.

It also explores particular types of sequence known as arithmetic progressions aps and geometric progressions gps, and the corresponding series. Consider the successive quotients that we obtain in the division of 10 by 3 at. Notes on infinite series pdf 61p currently this section contains no detailed description for the page, will update this page soon. If and l series is absolutely convergent, if l1 then the series is divergent, and if l1 then the test is inconclusive.

Now lets look at some special sequences, and their rules. For example, exponential growth is a growth pattern that is. Pupils need to have a good understanding of all number patterns and simultaneous equations from grade 10. A similar integral test would show that the series converges when q 1, while it diverges when q. A power series is like a polynomial of in nite degree. Since this is a geometric series, you can find the sum of the first 100 terms by using the formula sn a 1 1 n a r 1r. A series converges if the sequence of partial sums converges, and otherwise the series diverges. Prerequisite skills to be successful in this chapter, youll need to master. These are some notes on introductory real analysis. Powered by create your own unique website with customizable templates. Btw, that pdf was made by a mse user, and unless you knew italian, this years edition is the first in english. An infinite series is the indicated sum of the terms of an infinite sequence.