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Sequences: A sequence is of the form а1, а2, аз, а4, ... where the an are real numbers. Technically, a sequence is a function whose domain is the set of natural numbers, and whose range is a subset of the real numbers. Sequences may be defined in various ways: By listing, and appealing (via the three dots) to your intuition. Suppose the sequence is 1 2 2'5' 10' 17' 26 ' 37 3 4 5 6. Then the n-th term is An = Explicitly. For example, suppose an = n". Then a1 , а2 and az =

Sequences: A sequence is of the form а1, а2, аз, а4, ... where the an are real numbers. Technically, a sequence is a function whose domain is the set of natural numbers, and whose range is a subset of the real numbers. Sequences may be defined in various ways: By listing, and appealing (via the three dots) to your intuition. Suppose the sequence is 1 2 2'5' 10' 17' 26 ' 37 3 4 5 6. Then the n-th term is An = Explicitly. For example, suppose an = n". Then a1 , а2 and az =

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter1: Fundamental Concepts Of Algebra
Section1.2: Exponents And Radicals
Problem 91E
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Sequences: A sequence is of the form 19 а1, а2, аз, а4, where the an are real numbers. Technically, a sequence is a function whose domain is the set of natural numbers, and whose range is a subset of the real numbers. Sequences may be defined in various ways: By listing, and appealing (via the three dots) to your intuition. Suppose the sequence is 1 2 3 4 6 2'5' 10' 17’ 26 '37 Then the n-th term is An = Explicitly. For example, suppose an = n". Then a1 = a2 = and az = Recursively. For example, the Fibonacci Sequence is defined by а1 — а2 — 1, n = 2, 3, 4, .... An+1 = an + An-1, Thus az = and a5 = , A4 = Also a sequence may or may not have a limit. For the following sequences, enter the limit, or enter the letter "D" if the sequence diverges. an = n an n n²+4n-5 (2n-1)(3п—1) An
Transcribed Image Text:Sequences: A sequence is of the form 19 а1, а2, аз, а4, where the an are real numbers. Technically, a sequence is a function whose domain is the set of natural numbers, and whose range is a subset of the real numbers. Sequences may be defined in various ways: By listing, and appealing (via the three dots) to your intuition. Suppose the sequence is 1 2 3 4 6 2'5' 10' 17’ 26 '37 Then the n-th term is An = Explicitly. For example, suppose an = n". Then a1 = a2 = and az = Recursively. For example, the Fibonacci Sequence is defined by а1 — а2 — 1, n = 2, 3, 4, .... An+1 = an + An-1, Thus az = and a5 = , A4 = Also a sequence may or may not have a limit. For the following sequences, enter the limit, or enter the letter "D" if the sequence diverges. an = n an n n²+4n-5 (2n-1)(3п—1) An
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