Warm Up 1. 2. 3. 4. 5. 6. 7. 8. 9. DNE. 13.5 Sums of Infinite Series.

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

Warm UP! 1.Indentify the following as Arithmetic, Geometric, or neither: a.2, 5, 8, 11, … b.b. 2, 6, 24, … c.c. 5, 10, 20, 40, … 2. Demonstrate you know.
11.4 – Infinite Geometric Series. Sum of an Infinite Geometric Series.
Summation Notation.  Shorthand way of expressing a sum  Uses the Greek letter sigma: ∑ k is called the index of summation n is called the upper limit.
1.4 Infinite Geometric Series Learning Objective: to explore what happens when a geometric series is infinite and to express it using sigma notation. Warm-up.
Geometric Sequences and Series A sequence is geometric if the ratios of consecutive terms are the same. 2, 8, 32, 128, 512,... Definition of Geometric.
13.3 Arithmetic & Geometric Series. A series is the sum of the terms of a sequence. A series can be finite or infinite. We often utilize sigma notation.
9.2 Arithmetic Sequence and Partial Sum Common Difference Finite Sum.
Infinite Geometric Series
11.4 Geometric Sequences Geometric Sequences and Series geometric sequence If we start with a number, a 1, and repeatedly multiply it by some constant,
Homework Questions.
Aim: What are the arithmetic series and geometric series? Do Now: Find the sum of each of the following sequences: a)
9/8/2015Math SL1 - Santowski1 Lesson 30 - Summation Notation & Infinite Geometric Series Math SL1 - Santowski.
11.4 Series & Sigma Notation
Geometric Sequences and Series Unit Practical Application “The company has been growing geometrically”
Warm-up p 218 #3, 5, 7 and 9. Section 12-5: Sigma Notation and the n th Term In this section we will answer…  What notation can be used to indicate the.
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.
Lesson 4 - Summation Notation & Infinite Geometric Series
Rules Always answer in the form of a question Team names & buzzer sounds ready Points to be taken away for wrong answers? (Decide as a class…change this.
Sequences & Series. Sequences  A sequence is a function whose domain is the set of all positive integers.  The first term of a sequences is denoted.
13.3 – Arithmetic and Geometric Series and Their Sums Objectives: You should be able to…
Review of Sequences and Series.  Find the explicit and recursive formulas for the sequence:  -4, 1, 6, 11, 16, ….
1 1 OBJECTIVE At the end of this topic you should be able to Define sequences and series Understand finite and infinite sequence,
13.6 Sigma Notation. Objectives : 1. Expand sequences from Sigma Notation 2. Express using Sigma Notation 3. Evaluate sums using Sigma Notation Vocabulary.
Notes Over 11.1 Sequences and Series A sequence is a set of consecutive integers. A finite sequence contains a last term Infinite sequences continue without.
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.
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.
Arithmetic and Geometric Series: Lesson 43. LESSON OBJECTIVE: 1.Find sums of arithmetic and geometric series. 2.Use Sigma Notation. 3.Find specific terms.
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, …,
Warm up 1. Find the sum of : 2. Find the tenth term of the sequence if an = n2 +1: =
Aim: What is the arithmetic series ? Do Now: Find the sum of each of the following sequences: a) b)
SEQUENCES A sequence is a function whose domain in the set of positive integers. So if you have a function but limited the domain to the set of positive.
Math II UNIT QUESTION: How is a geometric sequence like an exponential function? Standard: MM2A2, MM2A3 Today’s Question: How do you recognize and write.
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.
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.
Geometric Series. In a geometric sequence, the ratio between consecutive terms is constant. The ratio is called the common ratio. Ex. 5, 15, 45, 135,...
Algebra II Honors Problem of the Day Homework: p odds Find the first 6 terms of the sequence defined as: Fibonacci!
11.2 Arithmetic Series. What is a series?  When the terms of a sequence are added, the indicated sum of the terms is called a series.  Example  Sequence.
Review of Sequences and Series
9.3 Geometric Sequences and Series. Common Ratio In the sequence 2, 10, 50, 250, 1250, ….. Find the common ratio.
Copyright © 2007 Pearson Education, Inc. Slide Geometric Series A geometric series is the sum of the terms of a geometric sequence. Sum of the.
Section 1: Sequences & Series /units/unit-10-chp-11-sequences-series
Unit 4: Sequences & Series 1Integrated Math 3Shire-Swift.
Section 13.6: Sigma Notation. ∑ The Greek letter, sigma, shown above, is very often used in mathematics to represent the sum of a series.
Copyright © 2012 Pearson Education, Inc. Publishing as Addison Wesley CHAPTER 8: Sequences, Series, and Combinatorics 8.1 Sequences and Series 8.2 Arithmetic.
Sequences and Series 9.1.
The sum of the infinite and finite geometric sequence
Geometric Sequences and Series (Section 8-3)
The symbol for summation is the Greek letter Sigma, S.
Finite Differences.
Section 11.1 Sequences and Series
Series and Summation Notation
DAY 30 AGENDA: Quiz Tues.
Lesson 3-1 Geometric Series
Section 1.6 Sigma Notations and Summation
Warm-up Write an equation whose limit at infinity does not exist
Geometric Sequences.
Warm Up Look for a pattern and predict the next number or expression in the list , 500, 250, 125, _____ 2. 1, 2, 4, 7, 11, 16, _____ 3. 1, −3,
Notes Over 11.1 Sequences and Series
Section 2.5 Sigma Notations and Summation
Sequences and Summation Notation
Warm Up Write an explicit formula for the following sequences.
Warm Up.
Warm Up Use summation notation to write the series for the specified number of terms …; n = 7.
1×1=1 11×11= ×111= ×1111= ×11111= ×111111= × = × =
Warm Up.
Warm Up Write the first 4 terms of each sequence:
Presentation transcript:

Warm Up DNE

13.5 Sums of Infinite Series

Classwork

a. b.

Classwork c. d.

2. Express … as an infinite geometric series. Find the sum. Classwork

13.6 Sigma Notation

SUMMATION NOTATION Often we want to sum the terms in a sequence so summation notation is a short-hand way express this. This number tells us what integer to start subbing in to create the terms in a sequence This number tells us when to stop (the last integer to sub in). This is the formula to sub into This sign means to sum up each of the terms in the sequence

Summation Notation  Ex: Evaluate the following sum:  Sol:

13.6 Sigma Notation

Try It:

Classwork Write in expanded form Evaluate

Classwork Write in expanded form

Classwork

Evaluate

Homework Page 502 #1-9 odds, #23-27 odds Page 508 #1-19 odds