Summation & Sigma Notation

Slides:



Advertisements
Similar presentations
9-4 Sequences & Series. Basic Sequences  Observe patterns!  3, 6, 9, 12, 15  2, 4, 8, 16, 32, …, 2 k, …  {1/k: k = 1, 2, 3, …}  (a 1, a 2, a 3, …,
Advertisements

MTH 252 Integral Calculus Chapter 6 – Integration Section 6.4 – The Definition of Area as a Limit; Sigma Notation Copyright © 2005 by Ron Wallace, all.
Summation Notation. Terminology The Greek letter, , indicates a sum and is referred to as a summation operation. k is referred to as the index of summation.
Summation Notation.  Shorthand way of expressing a sum  Uses the Greek letter sigma: ∑ k is called the index of summation n is called the upper limit.
5.7 Rational Exponents Fraction Exponents.
Sequences & Summation Notation 8.1 JMerrill, 2007 Revised 2008.
Factorial Notation For any positive integer n, n! means: n (n – 1) (n – 2)... (3) (2) (1) 0! will be defined as equal to one. Examples: 4! = =
Operations with Fractions
12.1 Sequences and Series ©2001 by R. Villar All Rights Reserved.
I CAN COMPARE AND ORDER RATIONAL NUMBERS BY USING A NUMBER LINE. 1.5 RATIONAL NUMBERS.
Section Summation & Sigma Notation. Sigma Notation  is the Greek letter “sigma” “Sigma” represents the capital “S”
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.
Sigma Notation. SUMMATION NOTATION Lower limit of summation (Starting point) Upper limit of summation (Ending point) SIGMA  equation.
Rational Exponents Fraction Exponents.
Scientific Notation. Simplify: Scientific Notation Expressed as a number between 0 and 10 times a power of positive - a very large number 10 negative.
Section 7.2 So far, we have only worked with integer exponents. In this section, we extend exponents to rational numbers as a shorthand notation when using.
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?
Write the first six terms of the following sequences.
11-4 INTRO TO SERIES DEFINITION A SERIES IS THE SUM OF THE TERMS OF A SEQUENCE. SEQUENCE VS. SERIES 2, 4, 8, … …
Warm Up: Section 2.11B Write a recursive routine for: (1). 6, 8, 10, 12,... (2). 1, 5, 9, 13,... Write an explicit formula for: (3). 10, 7, 4, 1,... (5).
Lesson 8.1 Page #1-25(EOO), 33, 37, (ODD), 69-77(EOO), (ODD), 99, (ODD)
Sequence – a function whose domain is positive integers. Section 9.1 – Sequences.
Slide Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley.
Objectives The student will be able to:  use Sigma Notation  find the mean absolute deviation of a data set SOL: A
Section 11.1 Sequences and Summation Notation Objectives: Definition and notation of sequences Recursively defined sequences Partial sums, including summation.
Chapter 11 Sequences, Induction, and Probability Copyright © 2014, 2010, 2007 Pearson Education, Inc Sequences and Summation Notation.
Arithmetic Series 19 May Summations Summation – the sum of the terms in a sequence {2, 4, 6, 8} → = 20 Represented by a capital Sigma.
11/10/2015.  Copy these definitions into your notes: 1. Rational number: Any number that can be put into the form of a fraction. 2. Irrational number:
MATHPOWER TM 12, WESTERN EDITION Chapter 6 Sequences and Series.
SEQUENCES OBJECTIVES: Write the first several terms of a sequence Write the terms of a sequence defined by a Recursive Formula Use Summation Notation Find.
Number Sets. Symbols for Number Set Counting numbers ( maybe 0, 1, 2, 3, 4, and so on) Natural Numbers: Positive and negative counting numbers (-2, -1,
Arithmetic Series Definitions & Equations Writing & Solving Arithmetic Series Practice Problems.
In this section, we will begin to look at Σ notation and how it can be used to represent Riemann sums (rectangle approximations) of definite integrals.
4.2 Area Definition of Sigma Notation = 14.
8.1 Sequences and Series Essential Questions: How do we use sequence notation to write the terms of a sequence? How do we use factorial notation? How.
11.2 Arithmetic Series. What is a series?  When the terms of a sequence are added, the indicated sum of the terms is called a series.  Example  Sequence.
Rational (fraction) Exponents Please READ as well as take notes & complete the problems followed in these slides.
Entry Task– Simplify Expand then solve 3 5, 3 4, 3 3, 3 2 and 3 1 on a separate line in your notebook Now do 3 -1, 3 -2, 3 -3, 3 -4 and 3 -5 but leave.
Problem of the Day The graph of a function f is shown above.Which of the following statements about f is false? A) f is continuous at x = a B) f has a.
ALGEBRA: FORM AND FUNCTION 2 nd edition by McCallum, Connally, Hughes-Hallett, et al.,Copyright 2015, John Wiley & Sons, Inc. Chapter 10 Summation Notation.
5.1 Areas and Distances. Area Estimation How can we estimate the area bounded by the curve y = x 2, the lines x = 1 and x = 3, and the x -axis? Let’s.
Algebra 2 Arithmetic Series. Algebra 2 Series – is the expression for the sum of the terms of a sequence.
5-4: Sigma Notation Objectives: Review sigma notation ©2002 Roy L. Gover
 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.
Warm Up DNE Sums of Infinite Series.
Series and Sequences An infinite sequence is an unending list of numbers that follow a pattern. The terms of the sequence are written a1, a2, a3,...,an,...
Sequences & Summation Notation
The symbol for summation is the Greek letter Sigma, S.
Math 2-1: Warm-up Evaluate each expression. 8 + (20 – 3)(2) 16 + (-9)
Finite Differences.
Copyright © 2014, 2010, 2007 Pearson Education, Inc.
Arithmetic Sequences and Series
7-5 Rational Exponents Fraction Exponents.
Section 11.1 Sequences and Series
Sigma/Summation Notation
SUMMATION or SIGMA NOTATION
9.1: Introduction to Sequences
9.1 Sequences Sequences are ordered lists generated by a
Notes Over 11.1 Sequences and Series
AREA Section 4.2.
Sequences and Summation Notation
7.1 Roots and Rational Exponents
Copyright © 2014, 2010, 2007 Pearson Education, Inc.
61 – Sequences and Series Day 2 Calculator Required
AREA Section 4.2.
10.1 Sequences and Summation Notation
Chapter 9 Section 1 (Series and Sequences)
Nth, Geometric, and Telescoping Test
Presentation transcript:

Summation & Sigma Notation Section 2.2.1 Summation & Sigma Notation

Sigma Notation Σ is the Greek letter sigma Sigma represents the capital “S” in English.

( values for k must be whole numbers or non- negative integers) Last number plugged in. Expanded form Sum Formula Index of summation.

Examples Write in expanded form and evaluate:

Examples Write in expanded form and evaluate:

Definition: Sigma Notation Upper Bound i th Term Index Lower Bound

Adding Rational Expressions Relative Prime Fractions: AKA Butterfly Method

Adding Rational Expressions:

Fractions with Common Factors:

Fractions with Common Factors:

Assignment Pg 72  #2-31 TO 2-45