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,

Slides:

Advertisements

Similar presentations

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

Advertisements

Series Brought to you by Tutorial Services – The Math Center.

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

The sum of the infinite and finite geometric sequence

Unit 7: Sequences and Series

A list of numbers following a certain pattern { a n } = a 1, a 2, a 3, a 4, …, a n, … Pattern is determined by position or by what has come before 3, 6,

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

State whether the sequence below is arithmetic, geometric or neither and then write the explicit definition of the sequence. 3, 7, 11, 15...

Geometric Sequences and Series

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

Notes Over 11.4 Infinite Geometric Sequences

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.

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.

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, ….

Summation Notation. Summation notation: a way to show the operation of adding a series of values related by an algebraic expression or formula. The symbol.

Infinite Geometric Series

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

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:

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.

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,...

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

Review of Sequences and Series

9.3 Geometric Sequences and Series. 9.3 Geometric Sequences A sequence is geometric if the ratios of consecutive terms are the same. This common ratio.

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.

Arithmetic vs. Geometric Sequences and how to write their formulas

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

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)

Arithmetic and Geometric

Sequence/Series 1. Find the nth term if, a1 = -1, d = 10, and n = 25 ________ 2. Find a12 for –17, -13, -9,... _________ 3. Find the missing terms in.

nth or General Term of an Arithmetic Sequence

11.3 – Geometric Sequences and Series

13.3 – Arithmetic and Geometric Series and Their Sums

Today in Precalculus Go over homework

Arithmetic and Geometric Series

8.1 and 8.2 Summarized.

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

Arithmetic Sequences and Series

Aim: What is the geometric series ?

Infinite Geometric Series

Arithmetic and Geometric

Infinite Geometric Series

Test the series for convergence or divergence. {image}

Unit 1 Test #3 Study Guide.

Test the series for convergence or divergence. {image}

Find the sums of these geometric series:

Representation of Functions by Power Series (9.9)

Homework Log Fri. 4/8 Lesson Rev Learning Objective:

Section 1.6 Sigma Notations and Summation

Geometric Sequences and Series

12.2 – Arithmetic Sequences and Series

Homework Questions.

Notes: 12-3 Infinite Sequences and Series

If the sequence of partial sums converges, the series converges

9.3 (continue) Infinite Geometric Series

12.2 – Arithmetic Sequences and Series

Geometric Sequences and Series

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

12.2 – Geometric Sequences and Series

Packet #29 Arithmetic and Geometric Sequences

12.1 – Arithmetic Sequences and Series

Homework Questions.

Presentation transcript:

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, and variable on bottom, the limit is 0. (ex 1/x 2, 1/x 3, 4/5x 2) Anytime you have a variable on top (2x, 3x, x/2) the limit is ∞, or Does Not Exist

Practice:

Convergent Series: An infinite series that approaches a limit Divergent Series: An infinite series that does not approach a limit. All arithmetic series are divergent In a geometric series, if lrl > 1, the series is divergent if lrl <1, the series is convergent

Add the following:

7)Find the sum of the series: /7-… 8) Find the sum of (6/5) + (4/5) + (8/15)+…