Copyright © 2007 Pearson Education, Inc. Slide 11-1 11-5 Geometric Series A geometric series is the sum of the terms of a geometric sequence. Sum of the.

Slides:



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

Slide Copyright © 2009 Pearson Education, Inc. Active Learning Lecture Slides For use with Classroom Response Systems © 2009 Pearson Education, Inc.
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.
© 2010 Pearson Education, Inc. All rights reserved.
Determine whether the sequence 6, 18, 54, is geometric. If it is geometric, find the common ratio. Choose the answer from the following :
Copyright © 2005 Pearson Education, Inc. Publishing as Pearson Addison-Wesley.
Copyright © 2008 Pearson Education, Inc. Chapter 12 Sequences and Series Copyright © 2008 Pearson Education, Inc.
Geometric Sequences and Series
Notes Over 11.3 Geometric Sequences
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,
Copyright © 2007 Pearson Education, Inc. Slide 8-1.
THE BEST CLASS EVER…ERRR…. PRE-CALCULUS Chapter 13 Final Exam Review.
Notes Over 11.4 Infinite Geometric Sequences
Copyright © 2011 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Chapter 8 Sequences and Infinite Series.
Copyright © 2007 Pearson Education, Inc. Slide 8-1.
Copyright © 2011 Pearson Education, Inc. Slide Sequences A sequence is a function that has a set of natural numbers (positive integers) as.
Copyright © 2011 Pearson Education, Inc. Slide
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.
Goal: Does a series converge or diverge? Lecture 24 – Divergence Test 1 Divergence Test (If a series converges, then sequence converges to 0.)
ADVANCED ALG/TRIG Chapter 11 – Sequences and Series.
Review of Sequences and Series.  Find the explicit and recursive formulas for the sequence:  -4, 1, 6, 11, 16, ….
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, …
Copyright © 2007 Pearson Education, Inc. Slide , 2, 4, 8, 16 … is an example of a geometric sequence with first term 1 and each subsequent term is.
Chapter 11 Sequences, Induction, and Probability Copyright © 2014, 2010, 2007 Pearson Education, Inc Sequences and Summation Notation.
Example Solution For each geometric sequence, find the common ratio. a)  2,  12,  72,  432,... b) 50, 10, 2, 0.4, 0.08,... SequenceCommon Ratio.
8.3 Geometric Sequences and Series Objectives: -Students will recognize, write, and find the nth terms of geometric sequences. -Students will find the.
Copyright © Cengage Learning. All rights reserved.
AP Calculus Miss Battaglia  An infinite series (or just a series for short) is simply adding up the infinite number of terms of a sequence. Consider:
One important application of infinite sequences is in representing “infinite summations.” Informally, if {a n } is an infinite sequence, then is an infinite.
Copyright © 2011 Pearson, Inc. 9.5 Series Goals: Use sigma notation to find the finite sums of terms in arithmetic and geometric sequences. Find sums of.
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,...
{ 12.3 Geometric Sequence and Series SWBAT evaluate a finite geometric series SWBAT evaluate infinite geometric series, if it exists.
Series A series is the sum of the terms of a sequence.
10.2 Summing an Infinite Series Feb Do Now Write the following in summation notation 1, ¼, 1/9, 1/16.
Review of Sequences and Series
Thursday, March 8 How can we use geometric sequences and series?
A LESSON BY U S PRAJAPATI, PGT MATH, KV KHAGAUL GEOMETRIC SEQUENCES AND SERIES.
Geometric Sequence – a sequence of terms in which a common ratio (r) between any two successive terms is the same. (aka: Geometric Progression) Section.
9.3 Geometric Sequences and Series. Common Ratio In the sequence 2, 10, 50, 250, 1250, ….. Find the common ratio.
Geometric Sequences and Series Notes 9.2. Notes 9.2 Geometric Sequences  a n =a 1 r n-1 a 1 is the first term r is the ratio n is the number of terms.
Splash Screen. Concept P. 683 Example 1A Convergent and Divergent Series A. Determine whether the infinite geometric series is convergent or divergent.
S ECT. 9-2 SERIES. Series A series the sum of the terms of an infinite sequence Sigma: sum of.
JEOPARDY! $100 $100 $100 $100 $100 $200 $200 $200 $200 $200 $300 $300
Series and Convergence (9.2)
Unit 6 Review.
The sum of the infinite and finite geometric sequence
Review Write an explicit formula for the following sequences.
Copyright © 2014, 2010, 2007 Pearson Education, Inc.
Sect.R10 Geometric Sequences and Series
Sequences and Infinite Series
© 2010 Pearson Education, Inc. All rights reserved
1.6A: Geometric Infinite Series
Use summation notation to write the series
How do I find the sum & terms of geometric sequences and series?
Find the sums of these geometric series:
Geometric Sequences.
Homework Questions.
9.3 (continue) Infinite Geometric Series
Copyright © 2006 Pearson Education, Inc
Determine whether the sequence converges or diverges. {image}
9.5 Series.
Geometric Sequences and Series
Warm Up.
Warm Up Use summation notation to write the series for the specified number of terms …; n = 7.
Packet #29 Arithmetic and Geometric Sequences
Warm Up.
Homework Questions.
Section 12.3 Geometric Sequences; Geometric Series
Presentation transcript:

Copyright © 2007 Pearson Education, Inc. Slide Geometric Series A geometric series is the sum of the terms of a geometric sequence. Sum of the First n Terms of a Geometric Sequence If a geometric sequence has first term a 1 and common ratio r, then the sum of the first n terms is given by where.

Copyright © 2007 Pearson Education, Inc. Slide 11-2 Evaluate the series to the given term.

Copyright © 2007 Pearson Education, Inc. Slide 11-3 Evaluate the series to the given term.

Copyright © 2007 Pearson Education, Inc. Slide Infinite Geometric Series Sum of the Terms of an Infinite Geometric Sequence The sum of the terms of an infinite geometric sequence with first term a 1 and common ratio r, where –1 < r < 1 is given by meaning it converges. If r > 1 or r < -1 then it does not converge. We call this diverge.

Copyright © 2007 Pearson Education, Inc. Slide 11-5 Decide whether each infinite geometric series converges or diverges then state whether it’ll have a sum … … …

Copyright © 2007 Pearson Education, Inc. Slide 11-6 Summation Notation for infinite geometric series

Copyright © 2007 Pearson Education, Inc. Slide 11-7 Evaluate each infinite series that has a sum

Copyright © 2007 Pearson Education, Inc. Slide 11-8 Evaluate each infinite series that has a sum

Copyright © 2007 Pearson Education, Inc. Slide 11-9 Evaluate each infinite series that has a sum

Copyright © 2007 Pearson Education, Inc. Slide Suppose your business made a profit of $4000 the first year. If the profit increases 25% per year, find the total profit over the first 6 years.