Understanding Series and Summation Notation in Mathematics
160 likes | 262 Views
Learn how to read and interpret sequences, understand series, summation properties, and application of notation in mathematical patterns. Practice calculating series sums and applying various properties.
Understanding Series and Summation Notation in Mathematics
E N D
Presentation Transcript
9.1 Series Objectives: Understand Notation!! Reading the language and symbols which ask you to add the terms of a sequence
Remember • Sequences are function- We use an equation to represent a sequence pattern • We used to use f(n), but we use an just to notate more clearly we are looking at patterns
Vocabulary • Series- The sum of a sequence Notated Sn : Means we need to add up the first n terms in a given sequence • Let an = a1 , a2, a3, a4, …, an • Then Sn= a1 + a2 + a3 + a4 + …+ an
Vocabulary • Summation Notation(Also called sigma notation) • What we will use to calculate a series- the sum of terms Read the SUM of the terms in the sequence an from term in position 1 to the term in position n Notation:
ai = a1 + a2 + a3 + a4 + a5 ai Thus we would add up terms in position 1 through 5
Example Page # 622 #76
Example 2 • Page 622 #89
Summation Properties • Consider an = 5 an = a1 5 a2 5 a3 5 a4 5 a5 5 + + + +
Property 1:The summation of a sequence given by a constant (c is a constant)
Summation Property 2 = 5(1) + 5(2) + 5(3) + 5(4) + 5(5) an = 5n = 5(1 + 2 + 3 + 4 + 5 )
Property 2:The summation of a sequence given by a scalar multiple (c is a constant scalar)Pull out the constant and find the sum Example:
Property 3:Summation of polynomials (addition/subtraction of many terms)
Property 3:Summation of polynomials (addition/subtraction of many terms)
