IBDP Mathematics Analysis & Approaches HL Chapter 3 Notes

Sequences and Series


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All DP mathematics courses serve to accommodate the diverse range of needs, interests and abilities of students, and to fulfill the requirements of various university and career aspirations. The aims of these courses are to enable students to: develop mathematical knowledge, concepts, principles, logical, critical and creative thinking, employ and refine their powers of abstraction and generalization. Students are also encouraged to appreciate the international dimensions of mathematics and the multiplicity of its cultural and historical perspectives

A sequence is a list of numbers that is written in a defined order, ascending or descending, following a specific rule. It can also be defined as a function whose domain is the set of positive integers. Ex. (1,2,6,8…), (1,4,9,16). Whereas a series is the sum of all the terms in a sequence. However, there has to be a definite relationship between all the terms of the sequence. Ex. (1+2+6+8….), (1+4+9+16…). In this chapter we learn about arithmetic and geometric sequences and series, the sum of finite and infinite sequences and series and lastly, the binomial theorem. In elementary algebra, the binomial theorem describes the algebraic expansion of powers of a binomial. In this chapter you will learn the following: Binomial expansion, The binomial theorem for n E z+ and the binomial theorem for n E Q. The sum a + b is called a binomial as it contains two terms. Any expression of the form (a + b) n is called a power of a binomial. You will also need to learn Pascal’s triangle to understand this chapter completely. As Pascal’s triangle cannot be used for large distributions, the use of binomial theorem is needed.