Series.

Slides:



Advertisements
Similar presentations
Chapter 8 Vocabulary. Section 8.1 Vocabulary Sequences An infinite sequence is a function whose domain is the set of positive integers. The function.
Advertisements

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.
A sequence is a set of numbers arranged in a definite order
CMSC 250 Discrete Structures Summation: Sequences and Mathematical Induction.
Geometric Sequences and Series
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.
Arithmetic Sequences and Series
Today’s Vocab : Today’s Agenda Sigma Partial Sum Infinite Series Finite Series HW: Worksheet14-2b Arithmetic and Geometric Sequences AND QUIZ corrections!!!
9.2 Arithmetic Sequence and Partial Sum Common Difference Finite Sum.
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.
Aim: What are the arithmetic series and geometric series? Do Now: Find the sum of each of the following sequences: a)
Arithmetic Sequences and Series
THE BEST CLASS EVER…ERRR…. PRE-CALCULUS Chapter 13 Final Exam Review.
Sequences & Series Pre-Calculus Lesson 9.1. Infinite Sequence: A sequence without bound - - 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, … ? (what’s next 2 terms)
Math 71B 11.1 – Sequences and Summation Notation 1.
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.
9-4 Arithmetic Series Today’s Objective: I can find the sum of an arithmetic series.
Sigma Notation. SUMMATION NOTATION Lower limit of summation (Starting point) Upper limit of summation (Ending point) SIGMA  equation.
ADVANCED ALG/TRIG Chapter 11 – Sequences and Series.
Notes 9.4 – Sequences and Series. I. Sequences A.) A progression of numbers in a pattern. 1.) FINITE – A set number of terms 2.) INFINITE – Continues.
Series Ch. 13.
Review of Sequences and Series.  Find the explicit and recursive formulas for the sequence:  -4, 1, 6, 11, 16, ….
By Sheldon, Megan, Jimmy, and Grant..  Sequence- list of numbers that usually form a pattern.  Each number in the list is called a term.  Finite sequence.
Geometric Sequences and Series Section Objectives Recognize, write, and find nth terms of geometric sequences Find the nth partial sums of geometric.
Aim: Summation Notation Course: Alg. 2 & Trig. Do Now: Aim: What is this symbol It’s Greek to me! Find the sum of the geometric series.
13.6 Sigma Notation. Objectives : 1. Expand sequences from Sigma Notation 2. Express using Sigma Notation 3. Evaluate sums using Sigma Notation Vocabulary.
Aim: What is the summation notation?
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.
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)
Warm up 1. Find the sum of : 2. Find the tenth term of the sequence if an = n2 +1: =
8.3 Geometric Sequences and Series Objectives: -Students will recognize, write, and find the nth terms of geometric sequences. -Students will find the.
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.
9.1 Sequences and Series. Definition of Sequence  An ordered list of numbers  An infinite sequence is a function whose domain is the set of positive.
Figure out how to work with infinite series when i=0 vs i=1 Slide 12.
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.
{ 12.3 Geometric Sequence and Series SWBAT evaluate a finite geometric series SWBAT evaluate infinite geometric series, if it exists.
A sequence is a set of numbers in a specific order
How do I find the sum & terms of geometric sequences and series?
Ivy Do, Christiana Kim, Julia O’Loughin, Tomoki Yagasaki.
Review of Sequences and Series
A LESSON BY U S PRAJAPATI, PGT MATH, KV KHAGAUL GEOMETRIC SEQUENCES AND SERIES.
13.3 Arithmetic and Geometric Series and Their Sums Finite Series.
9.3 Geometric Sequences and Series. Common Ratio In the sequence 2, 10, 50, 250, 1250, ….. Find the common ratio.
Unit 4: Sequences & Series 1Integrated Math 3Shire-Swift.
Arithmetic Sequences and Series Section Objectives Use sequence notation to find terms of any sequence Use summation notation to write sums Use.
 A sequence is a function whose domain is a set of consecutive integers. If a domain is not specified, it is understood that the domain starts with 1.
Essential Question: How do you find the nth term and the sum of an arithmetic sequence? Students will write a summary describing the steps to find the.
Arithmetic Sequences and Series
Geometric Sequences and Series
The sum of the infinite and finite geometric sequence
11.3 – Geometric Sequences and Series
Sect.R10 Geometric Sequences and Series
The symbol for summation is the Greek letter Sigma, S.
Aim: What is the geometric series ?
Finite Differences.
Unit 5 – Series, Sequences and Limits Section 5
Sigma Notation.
How do I find the sum & terms of geometric sequences and series?
10.2 Arithmetic Sequences and Series
Lesson 3-1 Geometric Series
Alternating signs means we have (-1)n-1 power.
Sequences and Summation Notation
9.5 Series.
Geometric Sequences and Series
Geometric Sequences and Series
Warm Up Use summation notation to write the series for the specified number of terms …; n = 7.
Chapter 9 Section 1 (Series and Sequences)
Presentation transcript:

Series

Summation Notation The sum of the first n terms of a sequence upper limit of summation index of summation equation

Properties

Series The sum of all terms of the infinite sequence is called an infinite series The sum of the first n terms of the sequence is called the finite series

Calculator How to… 2nd stat Sum(Seq(function, x, lower #, upper #)) Math Sum OPS Seq Sum(Seq(function, x, lower #, upper #))

Arithmetic Series Sum of a FINITE arithmetic sequence with n terms

Geometric Series Sum of a FINITE geometric sequence with n terms Sum of a INFINITE geometric sequence with n terms and r≠1