Warming Up. 13.5: Sums of Infinite Series Pre-Calculus.

Slides:

Advertisements

Similar presentations

Geometric Sequences and Series

Advertisements

9.2 – Arithmetic Sequences and Series

12.1 – Arithmetic Sequences and Series

What is the sum of the following infinite series 1+x+x2+x3+…xn… where 0

11.4 – Infinite Geometric Series. Sum of an Infinite Geometric Series.

Knight’s Charge  Quiz #1  When you finish your quiz, pick up the “INIFINITE GEO SERIES” worksheet and begin working on it! NOTE: The original segment.

13.1, 13.3 Arithmetic and Geometric Sequences and Series

13.7 Sums of Infinite Series. The sum of an infinite series of numbers (or infinite sum) is defined to be the limit of its associated sequence of partial.

Geometric Sequences and Series. Arithmetic Sequences ADD To get next term Geometric Sequences MULTIPLY To get next term Arithmetic Series Sum of Terms.

THE BEST CLASS EVER…ERRR…. PRE-CALCULUS Chapter 13 Final Exam Review.

Notes Over 11.4 Infinite Geometric Sequences

Infinite Geometric Series

7.4 Find Sums of Infinite Geometric Series

10.2 – Arithmetic Sequences and Series. An introduction … describe the pattern Arithmetic Sequences ADD To get next term Geometric Sequences MULTIPLY.

Intro to Infinite Series Geometric Series

12-5 Warm Up Lesson Presentation Lesson Quiz

EXAMPLE 4 Use an infinite series as a model Pendulums A pendulum that is released to swing freely travels 18 inches on the first swing. On each successive.

Advanced Precalculus Notes 11.3 Geometric Sequences; Geometric Series.

The purpose of this section is to discuss sums that contains infinitely many terms.

AP Calculus Objective: Understand definition of convergent infinite series and use properties of infinite geometric series.

Warm-up:  p 185 #1 – 7. Section 12-3: Infinite Sequences and Series In this section we will answer…  What makes a sequence infinite?  How can something.

Example: Finding the nth Term

EXAMPLE 4 Use an infinite series as a model Pendulums

Algebra II Unit 1 Lesson 2, 3 & 5

12.3 Geometric Sequences and Series ©2001 by R. Villar All Rights Reserved.

12.4: Infinite Geometric Series. What is the pattern? What are the next three terms? What’s going on with the “…”? Infinite Geometric Series: Notation:

Sequences Lesson 8.1. Definition A __________________ of numbers Listed according to a given ___________________ Typically written as a 1, a 2, … a n.

Warm Up In the Practice Workbook… Practice 8-8 (p. 110) # 4 a – d.

9.1 Part 1 Sequences and Series.

Series and Convergence Lesson 9.2. Definition of Series Consider summing the terms of an infinite sequence We often look at a partial sum of n terms.

ALGEBRA II CONVERGENT GEOMETRIC SERIES.

Standard Accessed: Students will analyze sequences, find sums of series, and use recursive rules.

{ 12.3 Geometric Sequence and Series SWBAT evaluate a finite geometric series SWBAT evaluate infinite geometric series, if it exists.

SECTION REVIEW Arithmetic and Geometric Sequences and Series.

9.1 Power Series Quick Review What you’ll learn about Geometric Series Representing Functions by Series Differentiation and Integration Identifying.

How do I find the sum & terms of geometric sequences and series?

Copyright © by Houghton Mifflin Company, Inc. All rights reserved. 1 Definition of Sequence You find a job that pays an annual salary of $32,000 with an.

Arithmetic Sequences Objective:

11-5 Geometric Series Hubarth Algebra II. A geometric series is the expression for the sum of the terms of a geometric sequence. As with arithmetic series,

Section 12.3 – Infinite Series. 1, 4, 7, 10, 13, …. Infinite Arithmetic No Sum 3, 7, 11, …, 51 Finite Arithmetic 1, 2, 4, …, 64 Finite Geometric 1, 2,

Infinite Series Lesson 8.5. Infinite series To find limits, we sometimes use partial sums. If Then In other words, try to find a finite limit to an infinite.

13.5 – Sums of Infinite Series Objectives: You should be able to…

Infinite Geometric Series. Find sums of infinite geometric series. Use mathematical induction to prove statements. Objectives.

Chapter 1: Limits. Section 1.1:Limit of a Sequence An infinite sequence is the range of a function which has the set of natural numbers as its domain.

WARM UP Infinite Geometric Series EQ: When does an infinite geometric series have a sum and when does it not have a sum? Assessment: Students will.

PreCalculus 8-R Unit 8 Sequences, Series and Probability Review Problems.

12.1 – Arithmetic Sequences and Series

Sum it up Jeff Bivin -- LZHS.

Geometric Sequences and Series

Infinite Sequences and Series

Lake Zurich High School

Infinite Geometric Series

Unit 5 – Series, Sequences and Limits Section 5

Infinite Geometric Series

How do I find the sum & terms of geometric sequences and series?

Sequences and Series Review Get into groups of 4!

12.3 – Geometric Sequences and Series

Section 11.2 – Sequences and Series

Section 11.2 – Sequences and Series

Find the sum of , if it exists.

Find the sums of these geometric series:

Series and Convergence

Warm-Up Find the sum of the infinite geometric series, if it exists.

Slides for 5/10 & 5/11 Precalculus.

64 – Infinite Series Calculator Required

Geometric Series.

65 – Infinite Series Calculator Required

Lake Zurich High School

Objectives Find sums of infinite geometric series.

12.3 – Geometric Sequences and Series

Presentation transcript:

Warming Up

13.5: Sums of Infinite Series Pre-Calculus

Objectives : 1. Evaluate Infinite Series 2. Find interval of convergence 3. Evaluate repeating decimals Vocabulary : converge, diverge, interval of convergence 13.5 Sum of Infinite Series

Learning the Lingo/ Rules

Example: Find the sum of the infinite geometric series: 9 – – …

Quick Practice! Find the sum of the given infinite series, otherwise state that it diverges! 10/9

Explain why the series converges or diverges. Show mathematical proof …

Solution (1 < x < 3) is called the “interval of convergence”

For what values of x does the following infinite series converge? -1 < x < 1

The Bouncing Ball Problem – Version A A ball is dropped from a height of 50 feet. It rebounds 4/5 of it’s height, and continues this pattern until it stops. What is the total vertical distance that the ball will travel before it stops? / /5

An old grandfather clock is broken. When the pendulum is swung it follows a swing pattern of 25 cm, 20 cm, 16 cm, and so on until it comes to rest. What is the total distance the pendulum swings before coming to rest?

The Bouncing Ball Problem – Version B A ball is thrown 100 feet into the air. It rebounds 3/4 of it’s height, and continues this pattern until it stops. What is the total vertical distance that the ball will travel before it stops? / /4

Practice TB P.502: 1-17 odd, 33, 34, 39, 40