Infinite Geometric Series

Slides:

Advertisements

Similar presentations

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

Advertisements

What’s Your Guess? Chapter 9: Review of Convergent or Divergent Series.

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

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

12-3 Infinite Sequences and Series. Hints to solve limits: 1)Rewrite fraction as sum of multiple fractions Hint: anytime you have a number on top,

11.3 Geometric Sequences.

Introduction We have seen series that are finite, meaning they have a limited number of terms, but what happens to a series that has infinite terms? A.

Infinite Geometric Series. Write in sigma notation

Infinite Geometric 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.

Section 11-1 Sequences and Series. Definitions A sequence is a set of numbers in a specific order 2, 7, 12, …

Geometric Sequences and Series

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

Notes Over 11.4 Infinite Geometric Sequences

Intro to Infinite Series Geometric Series

12-5 Warm Up Lesson Presentation Lesson Quiz

Splash Screen. Lesson Menu Five-Minute Check (over Lesson 10–3) CCSS Then/Now New Vocabulary Key Concept: Convergent and Divergent Series Example 1:Convergent.

Series and Convergence

12.4 – Find Sums of Infinite Geometric Series. Think about this… What will happen when n becomes really big? It will get closer and closer to zero.

Day 4 Notes Infinite Geometric Series. The Sum of an Infinite Geometric Series If the list of terms goes on infinitely, how is it possible to add them.

13.2Series. Sequence 2, 4, 6, …, 2n, … A sequence is a list. Related finite series Related infinite series … + 2n + … Series.

9.1 Part 1 Sequences and Series.

Infinite Geometric Series

SERIES: PART 1 Infinite Geometric Series. Progressions Arithmetic Geometric Trigonometric Harmonic Exponential.

Section 8.2: Infinite Series. Zeno’s Paradox Can you add infinitely many numbers ?? You can’t actually get anywhere because you always have to cover half.

Warm Up 2. Consider the series: a)What is the sum of the series? b)How many terms are required in the partial sum to approximate the sum of the infinite.

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,...

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

Series A series is the sum of the terms of a sequence.

Review of Sequences and Series

Fractions and Decimal Fractions Fractions Decimal Fractions

Geometric Sequence – a sequence of terms in which a common ratio (r) between any two successive terms is the same. (aka: Geometric Progression) Section.

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.

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

Splash Screen. Concept P. 683 Example 1A Convergent and Divergent Series A. Determine whether the infinite geometric series is convergent or divergent.

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

12. Section 10.2 Summing an Infinite Series Continued.

Section 1: Sequences & Series /units/unit-10-chp-11-sequences-series

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.

Thursday, March 31MAT 146. Thursday, March 31MAT 146 Our goal is to determine whether an infinite series converges or diverges. It must do one or the.

Lesson 69 – Ratio Test & Comparison Tests

S ECT. 9-2 SERIES. Series A series the sum of the terms of an infinite sequence Sigma: sum of.

Series and Convergence (9.2)

nth or General Term of an Arithmetic Sequence

Today in Precalculus Go over homework

Arithmetic and Geometric Series

Infinite GP’s.

Aim: What is the geometric series ?

Infinite Geometric Series

Infinite Geometric Series

Use the Integral Test to determine which of the following series is divergent. 1. {image}

Limits What does this mean?.

Test the series for convergence or divergence. {image}

Lesson 64 – Ratio Test & Comparison Tests

1.6A: Geometric Infinite Series

Find the sum of , if it exists.

Test the series for convergence or divergence. {image}

Find the sums of these geometric series:

Homework Questions.

If the sequence of partial sums converges, the series converges

9.3 (continue) Infinite Geometric Series

Which of the given series is(are) convergent?

Which of the given series is(are) convergent?

Objectives Find sums of infinite geometric series.

Warm Up Use summation notation to write the series for the specified number of terms …; n = 7.

Homework Questions.

Presentation transcript:

Infinite Geometric Series

Infinite Geometric Series 1 + 0.5 + 0.25 + 0.125 +0.0625 + ... S4 = S5 = S9 =

Infinite Geometric Series 1 + 0.5 + 0.25 + 0.125 +0.0625 + ... An infinite geometric series has an infinite number of terms S17 = S28 = A series that has a sum is a convergent series

Infinite Geometric Series Convergent series | r | < 1

Infinite Geometric Series 1 + 2 + 4 + 8 + 16 + ... S5 = 31 S9 = 511 S15 = 32767

Infinite Geometric Series 1 + 2 + 4 + 8 + 16 + ... A series that does not have a sum is a divergent series

Infinite Geometric Series Divergent series | r | ≥ 1

When | r | < 1 (r n)will approach 0 Infinite Geometric Series Sum of an Infinite Geometric Series When | r | < 1 (r n)will approach 0

When | r | ≥ 1 The Series has no Sum Infinite Geometric Series Sum of an Infinite Geometric Series When | r | ≥ 1 The Series has no Sum

If a Series goes to infinity Infinite Geometric Series If a Series goes to infinity The infinity symbol ∞ is placed above the Σ

Infinite Geometric Series a1 r

Write as a fraction Write a Repeating Decimal as Fraction Infinite Geometric Series Write a Repeating Decimal as Fraction Write as a fraction

Infinite Geometric Series

Infinite Geometric Series