13.6 Sigma Notation. Objectives : 1. Expand sequences from Sigma Notation 2. Express using Sigma Notation 3. Evaluate sums using Sigma Notation Vocabulary.

Slides:

Advertisements

Similar presentations

Arithmetic Series Vocabulary series: the sum of the indicated terms in a sequence arithmetic series: the sum of an arithmetic sequence.

Advertisements

The sum of the infinite and finite geometric sequence

Assignment Answers: Find the partial sum of the following: 1. = 250/2 ( ) = 218, = 101/2 (1/2 – 73/4) = Find the indicated n th.

9.2 Arithmetic Sequence and Partial Sum Common Difference Finite Sum.

Arithmetic Sequences and Series

Factorial Notation For any positive integer n, n! means: n (n – 1) (n – 2)... (3) (2) (1) 0! will be defined as equal to one. Examples: 4! = =

Section Summation & Sigma Notation. Sigma Notation  is the Greek letter “sigma” “Sigma” represents the capital “S”

SEQUENCES AND SERIES Arithmetic. Definition A series is an indicated sum of the terms of a sequence.  Finite Sequence: 2, 6, 10, 14  Finite Series:2.

Sigma Notation. SUMMATION NOTATION Lower limit of summation (Starting point) Upper limit of summation (Ending point) SIGMA  equation.

12.5 Sigma Notation and the nth term

Sigma Notation A compact way of defining a series A series is the sum of a sequence.

12.5 – Sigma Notation. Quick Notes about the test All formulas will be given to you Mainly a 1 day test – Wed, 3/9 The Ratio Test will be on it: Just.

Aim: Summation Notation Course: Alg. 2 & Trig. Do Now: Aim: What is this symbol It’s Greek to me! Find the sum of the geometric series.

Aim: What is the summation notation?

4.7 Define & Use Sequences & Series. Vocabulary  A sequence is a function whose domain is a set of consecutive integers. If not specified, the domain.

Write the first six terms of the following sequences.

11-4 INTRO TO SERIES DEFINITION A SERIES IS THE SUM OF THE TERMS OF A SEQUENCE. SEQUENCE VS. SERIES 2, 4, 8, … …

9.1 Sequences and Series. A sequence is a collection of numbers that are ordered. Ex. 1, 3, 5, 7, …. Finding the terms of a sequence. Find the first 4.

ALGEBRA II INTRODUCTION TO SERIES. SERIES : The sum of part (partial) or all of the terms of a sequence. The sequence 3, 8, 13, 18 can be written.

Arithmetic and Geometric Series: Lesson 43. LESSON OBJECTIVE: 1.Find sums of arithmetic and geometric series. 2.Use Sigma Notation. 3.Find specific terms.

Sequences, Series, and Sigma Notation. Find the next four terms of the following sequences 2, 7, 12, 17, … 2, 5, 10, 17, … 32, 16, 8, 4, …

Lesson 8.1 Page #1-25(EOO), 33, 37, (ODD), 69-77(EOO), (ODD), 99, (ODD)

Sequence – a function whose domain is positive integers. Section 9.1 – Sequences.

Pg. 395/589 Homework Pg. 601#1, 3, 5, 7, 8, 21, 23, 26, 29, 33 #43x = 1#60see old notes #11, -1, 1, -1, …, -1#21, 3, 5, 7, …, 19 #32, 3/2, 4/3, 5/4, …,

Sequences Math 4 MM4A9: Students will use sequences and series.

Sequences and Summations

Review Write an explicit formula for the following sequences.

Summation & Sigma Notation

Chapter 11 Sequences, Induction, and Probability Copyright © 2014, 2010, 2007 Pearson Education, Inc Sequences and Summation Notation.

Arithmetic Series 19 May Summations Summation – the sum of the terms in a sequence {2, 4, 6, 8} → = 20 Represented by a capital Sigma.

Aim: What is the arithmetic series ? Do Now: Find the sum of each of the following sequences: a) b)

MATHPOWER TM 12, WESTERN EDITION Chapter 6 Sequences and Series.

Lesson 10.1, page 926 Sequences and Summation Notation Objective: To find terms of sequences given the nth term and find and evaluate a series.

9.1 Sequences and Series. Definition of Sequence  An ordered list of numbers  An infinite sequence is a function whose domain is the set of positive.

Series Section Intro to Series Series A sum of the terms of a sequence is called a series. A series is a finite series if it is the sum of a finite.

SEQUENCES OBJECTIVES: Write the first several terms of a sequence Write the terms of a sequence defined by a Recursive Formula Use Summation Notation Find.

2.3 Addition of Rational Numbers Day 2. Vocabulary Additive Inverse: Two rational numbers whose sum is 0 Property of Additive Inverse: a + (-a) =0.

8.3 Arithmetic Series. When the terms of a sequence are, the resulting expression is a series. Example: Sequence: 3, 6, 9, 12, 15 Series:

4.2 Area Definition of Sigma Notation = 14.

Algebra II Honors Problem of the Day Homework: p odds Find the first 6 terms of the sequence defined as: Fibonacci!

Arithmetic Sequences and Series Section Objectives Use sequence notation to find terms of any sequence Use summation notation to write sums Use.

5-4: Sigma Notation Objectives: Review sigma notation ©2002 Roy L. Gover

Warm Up DNE Sums of Infinite Series.

9.1 Series Objectives: Understand Notation!! Reading the language and symbols which ask you to add the terms of a sequence.

Holt McDougal Algebra 2 Introduction to Sequences Holt Algebra 2Holt McDougal Algebra 2 How do we find the nth term of a sequence? How do we write rules.

The sum of the infinite and finite geometric sequence

The symbol for summation is the Greek letter Sigma, S.

Tuesday, March 6 Essential Questions

Sequences and Series Section 8.1.

Finite Differences.

Copyright © 2014, 2010, 2007 Pearson Education, Inc.

Arithmetic Sequences and Series

Sigma Notation.

ANATOMY OF SIGMA: summation notation

Series and Summation Notation

Lesson 3-1 Geometric Series

Section 1.6 Sigma Notations and Summation

Sigma/Summation Notation

SUMMATION or SIGMA NOTATION

9.1: Introduction to Sequences

6.3 Geometric Series (get a calculator)

Notes Over 11.1 Sequences and Series

Sequences and Summation Notation

Summation Notation.

Copyright © 2014, 2010, 2007 Pearson Education, Inc.

61 – Sequences and Series Day 2 Calculator Required

10.1 Sequences and Summation Notation

Chapter 9 Section 1 (Series and Sequences)

Nth, Geometric, and Telescoping Test

Presentation transcript:

13.6 Sigma Notation

Objectives : 1. Expand sequences from Sigma Notation 2. Express using Sigma Notation 3. Evaluate sums using Sigma Notation Vocabulary : Sigma Notation, Index, Limit 13.6 Sigma Notation

Index Limits of the summation (upper limit) Summand/Rule Limits of the summation (lower limit) Learning the Lingo

Terms of the series Learning the Lingo

Problem Type One: Write the given series in expanded form.

Problem Type Two: Express the given series using sigma notation.

Problem Type Two: Express the given series using sigma notation … + 1

Problem Type Two: Express the given series using sigma notation.

Problem Type Two: Express the given series using sigma notation

Problem Type Three: Evaluate 76

Problem Type Three: Evaluate

Problem Type Three: Evaluate 2

ASSIGNMENT Page 508 FIND SUM FOR 4 and 5 and # 7, 11, 17, 19, 21a, 25