1. 1 zanariah @ump.edu.my 1 OBJECTIVE At the end of this topic you should be able to Define sequences and series Understand finite and infinite sequence, finite and infinite series Use the sum notation to write a series

2. Sequences and Series Sequence: function whose domain is the set of positive integers. a 1, a 2, a 3, a 4,..., a n,... are the terms of the sequence. If the domain only contains n positive integers, the sequence is a finite sequence.

3. What about this one?  What will the next number be? 0, 3, 6, 9, 12, 15, ___________ What’s the next number? What’s the next number? 5, 3, 1, -1, -3, -5, -7, _______________

4. Example: Find the first five terms of the sequence a n = 2n – 3 a 1 = 2(1) – 3 = –1 a 2 = 2(2) – 3 = 1 a 3 = 2(3) – 3 = 3 a 4 = 2(4) – 3 = 5 a 5 = 2(5) – 3 = 7 – {–1, 1, 3, 5, 7} A recursive function is a function whose domain is the set of non-negative integers. A well known recursive function is the factorial function. (We use an exclamation mark to denote a factorial)...

5. Sequences and Series

6. Factorials The factorial n! is defined for a positive integer n as n!=n(n-1)...2·1. So, for example, 4!=4·3·2·1=24

7. To write the sum of a finite sequence, we can use summation notation. This is also called Sigma Notation. Here’s an example of an expression in Sigma notation: Greek letter Sigma The expression formed by adding the first n terms of a sequence is called a series.

8. Example: Write the series represented by the summation notation. Then find the sum. The notation means “The sum from n = 1 to 5 of 2n” = 2(1) + 2(2) + 2(3) + 2(4) + 2(5) = 2 + 4 + 6 + 8 + 10 = 30

9. Ex. Write the series represented by the summation notation. Then find the sum. = 32