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12.3 Infinite Sequences and Series
Infinite sequence – a sequence that has infinitely many terms.Limits can be used to determine if a sequence approaches a value.
When any positive power of n appears only in the denominator of a fraction and n approaches infinity, the limit equals zero.
Ex 1 Estimate the limit of
For sequences with more complicated general formsFor sequences with more complicated general forms. Applications of the following limit theorems can make the limit easier to find.
Ex 2 Find the limit
Ex 3 find the limit
Limits don’t exist for all infinite sequencesLimits don’t exist for all infinite sequences. If the absolute value of a sequence becomes arbitrarily great or if the terms don’t approach a value the sequence has no limit. EX 4
When n is even, (-1)n = 1 and when n is odd, (-1)n = -1When n is even, (-1)n = 1 and when n is odd, (-1)n = -1. Therefore the sequence would have no limit.
Sum of an Infinite Series – if Sn is the sum of the first n terms and S is a number such that S – Sn approaches zero as n increases without bound, then the sum of the infinite series is S.
Sum of an Infinite Geometric Series
Ex 6 find the sum of …
Ex 7 write …as a fraction
Section 9.1 – Sequences.
What is the sum of the following infinite series 1+x+x2+x3+…xn… where 0
11.3: Geometric Sequences & Series
Series Brought to you by Tutorial Services – The Math Center.
9.4 Radius of Convergence Abraham Lincoln’s Home Springfield, Illinois.
11.4 – Infinite Geometric Series. Sum of an Infinite Geometric Series.
CN College Algebra Ch. 11: Sequences 11.3: Geometric Sequences Goals: Determine if a sequence is geometric. Find a formula for a geometric sequence. Find.
Chapter 8 Sec 3 Geometric Sequences and Series. 2 of 15 Pre Calculus Ch 8.3 Essential Question How do you find terms and sums of geometric sequences?
Warm up 1. Find the tenth term in the sequence: 2. Find the sum of the first 6 terms of the geometric series … If r=-2 and a 8 =
Infinite Series 9 Copyright © Cengage Learning. All rights reserved.
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.
Estimating Fraction Sums & Differences Textbook page 236 IAN page 68.
1.4 Infinite Geometric Series Learning Objective: to explore what happens when a geometric series is infinite and to express it using sigma notation. Warm-up.
Geometric Sequences and Series
Notes Over 11.3 Geometric Sequences
9.2 (Larson Book) Nth term test Geometric series Telescoping series Greg Kelly, Hanford High School, Richland, WashingtonPhoto by Vickie Kelly, 2003.
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.
Geometric Sequences and Series Part III. Geometric Sequences and Series The sequence is an example of a Geometric sequence A sequence is geometric if.
EXAMPLE 1 Find partial sums SOLUTION S 1 = 1 2 = 0.5 S 2 = = S 3 = Find and graph the partial sums S n for n = 1,
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