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Math Calculus Calculus

Using a Sequence Consider the sequence { a n } , where a 1 = k , a n − 1 = k + a n , and k > 0 (a) Show that { a n } is increasing and bounded. (b) Prove that lim n → ∞ a n exists. (c) Find lim n → ∞ a n

Using a Sequence Consider the sequence { a n } , where a 1 = k , a n − 1 = k + a n , and k > 0 (a) Show that { a n } is increasing and bounded. (b) Prove that lim n → ∞ a n exists. (c) Find lim n → ∞ a n

Solution Summary: The author explains that the sequence lefta_nright keeps on increasing and is bounded. The monotonicity is verified by an arithmetical induction.

Calculus

11th Edition

ISBN: 9780357246412

Author: Ron Larson; Bruce H. Edwards

Publisher: Cengage Limited

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Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence. It was invented by German mathematician Carl Friedrich Gauss.

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Textbook Question

Chapter 9.1, Problem 84E

Using a Sequence Consider the sequence { a n } , where a 1 = k , a n − 1 = k + a n , and k > 0

(a) Show that { a n } is increasing and bounded.

(b) Prove that lim n → ∞ a n exists.

(c) Find lim n → ∞ a n

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Chapter 9.1, Problem 83E

Chapter 9.1, Problem 85E

Chapter 9 Solutions

Calculus

Ch. 9.1 - CONCEPT CHECK Recursively Defined Sequence What...Ch. 9.1 - Prob. 2E Ch. 9.1 - Prob. 3E Ch. 9.1 - Prob. 4E Ch. 9.1 - Writing the Terms of a Sequence In Exercises 510,...Ch. 9.1 - Prob. 6E Ch. 9.1 - Writing the Terms of a Sequence In Exercises 510,...Ch. 9.1 - Prob. 8E Ch. 9.1 - Prob. 9E Ch. 9.1 - Prob. 10E

Ch. 9.1 - Writing the Terms of a Sequence In Exercises 11...Ch. 9.1 - Prob. 12E Ch. 9.1 - Prob. 13E Ch. 9.1 - Matching In Exercises 13-16, match the sequence...Ch. 9.1 - Prob. 15E Ch. 9.1 - Prob. 16E Ch. 9.1 - Prob. 17E Ch. 9.1 - Prob. 18E Ch. 9.1 - Prob. 19E Ch. 9.1 - Simplifying Factorials In Exercises 1720, simplify...Ch. 9.1 - Prob. 21E Ch. 9.1 - Prob. 22E Ch. 9.1 - Prob. 23E Ch. 9.1 - Finding the Limit of a Sequence In Exercises 2124,...Ch. 9.1 - Prob. 25E Ch. 9.1 - Prob. 26E Ch. 9.1 - Prob. 27E Ch. 9.1 - Prob. 28E Ch. 9.1 - Determining Convergence or Divergence In Exercises...Ch. 9.1 - Determining Convergence or Divergence In Exercises...Ch. 9.1 - Prob. 31E Ch. 9.1 - Prob. 32E Ch. 9.1 - Prob. 33E Ch. 9.1 - Determining Convergence or Divergence In Exercises...Ch. 9.1 - Prob. 35E Ch. 9.1 - Prob. 36E Ch. 9.1 - Prob. 37E Ch. 9.1 - Prob. 38E Ch. 9.1 - Prob. 39E Ch. 9.1 - Prob. 40E Ch. 9.1 - Prob. 41E Ch. 9.1 - Determining Convergence or Divergence In Exercises...Ch. 9.1 - Prob. 43E Ch. 9.1 - Determining Convergence or Divergence In Exercises...Ch. 9.1 - Finding the n th Term of a Sequence In Exercises...Ch. 9.1 - Prob. 46E Ch. 9.1 - Finding the n th Term of a Sequence In Exercises...Ch. 9.1 - Prob. 48E Ch. 9.1 - Finding the nth Term of a Sequence In Exercises...Ch. 9.1 - Finding the n th Term of a Sequence In Exercises...Ch. 9.1 - Finding the nth Term of a Sequence In Exercises...Ch. 9.1 - Finding the nth Term of a Sequence In Exercises...Ch. 9.1 - Prob. 53E Ch. 9.1 - Prob. 54E Ch. 9.1 - Prob. 55E Ch. 9.1 - Monotonic and Bounded Sequences In Exercises...Ch. 9.1 - Prob. 57E Ch. 9.1 - Prob. 58E Ch. 9.1 - Prob. 59E Ch. 9.1 - Prob. 60E Ch. 9.1 - Prob. 61E Ch. 9.1 - Prob. 62E Ch. 9.1 - Prob. 63E Ch. 9.1 - Prob. 64E Ch. 9.1 - Prob. 65E Ch. 9.1 - Prob. 66E Ch. 9.1 - Prob. 67E Ch. 9.1 - Government Expenditures A government program that...Ch. 9.1 - EXPLORING CONCEPTS Writing a Sequence Give an...Ch. 9.1 - Prob. 70E Ch. 9.1 - Prob. 71E Ch. 9.1 - HOW DO YOU SEE IT? The graph, of two sequences are...Ch. 9.1 - Prob. 73E Ch. 9.1 - Prob. 74E Ch. 9.1 - Prob. 75E Ch. 9.1 - Prob. 76E Ch. 9.1 - Prob. 77E Ch. 9.1 - Prob. 78E Ch. 9.1 - Prob. 79E Ch. 9.1 - Prob. 80E Ch. 9.1 - Fibonacci Sequence In a study of the progeny of...Ch. 9.1 - Prob. 82E Ch. 9.1 - Prob. 83E Ch. 9.1 - Using a Sequence Consider the sequence an, where...Ch. 9.1 - Prob. 85E Ch. 9.1 - Prob. 86E Ch. 9.1 - Prob. 87E Ch. 9.1 - Prob. 88E Ch. 9.1 - Prob. 89E Ch. 9.1 - Prob. 90E Ch. 9.1 - Prob. 91E Ch. 9.2 - Sequence and Series Describe the difference...Ch. 9.2 - Geometric Series Define a geometric series, State...Ch. 9.2 - Limit of the nth term of a Series The limit of the...Ch. 9.2 - Prob. 4E Ch. 9.2 - Finding Partial Sums In Exercises 5-10, find the...Ch. 9.2 - Finding Partial Sums In Exercises 5-10, find the...Ch. 9.2 - Prob. 7E Ch. 9.2 - Prob. 8E Ch. 9.2 - Prob. 9E Ch. 9.2 - Prob. 10E Ch. 9.2 - Prob. 11E Ch. 9.2 - Prob. 12E Ch. 9.2 - Prob. 13E Ch. 9.2 - Verifying Divergence In Exercises 11-18.verify...Ch. 9.2 - Verifying Divergence In Exercises 11-18.verify...Ch. 9.2 - Prob. 16E Ch. 9.2 - Prob. 17E Ch. 9.2 - Prob. 18E Ch. 9.2 - Prob. 19E Ch. 9.2 - Prob. 20E Ch. 9.2 - Prob. 21E Ch. 9.2 - Verifying Convergence In Excretes 19-24, verify...Ch. 9.2 - Prob. 23E Ch. 9.2 - Prob. 24E Ch. 9.2 - Prob. 25E Ch. 9.2 - Prob. 26E Ch. 9.2 - Prob. 27E Ch. 9.2 - Prob. 28E Ch. 9.2 - Prob. 29E Ch. 9.2 - Finding the Sum of a Convergent Series In...Ch. 9.2 - Prob. 31E Ch. 9.2 - Finding the Sum of a Convergent Series In...Ch. 9.2 - Finding the Sum of a Convergent Series In...Ch. 9.2 - Finding the Sum of a Convergent Series In...Ch. 9.2 - Prob. 35E Ch. 9.2 - Prob. 36E Ch. 9.2 - Prob. 37E Ch. 9.2 - Prob. 38E Ch. 9.2 - Prob. 39E Ch. 9.2 - Prob. 40E Ch. 9.2 - Prob. 41E Ch. 9.2 - Prob. 42E Ch. 9.2 - Prob. 43E Ch. 9.2 - Using a Geometric Series In Exercises 3944, (a)...Ch. 9.2 - Prob. 45E Ch. 9.2 - Prob. 46E Ch. 9.2 - Determining Convergence or Divergence In Exercises...Ch. 9.2 - Prob. 48E Ch. 9.2 - Determining Convergence or Divergence In Exercises...Ch. 9.2 - Prob. 50E Ch. 9.2 - Determining Convergence or Divergence In Exercises...Ch. 9.2 - Determining Convergence or Divergence In Exercises...Ch. 9.2 - Determining Convergence or Divergence In Exercises...Ch. 9.2 - Prob. 54E Ch. 9.2 - Prob. 55E Ch. 9.2 - Prob. 56E Ch. 9.2 - Prob. 57E Ch. 9.2 - Prob. 58E Ch. 9.2 - Prob. 59E Ch. 9.2 - Prob. 60E Ch. 9.2 - Prob. 61E Ch. 9.2 - Prob. 62E Ch. 9.2 - Prob. 63E Ch. 9.2 - Prob. 64E Ch. 9.2 - Making a Series Converge In Exercises 61-66, find...Ch. 9.2 - Prob. 66E Ch. 9.2 - Prob. 67E Ch. 9.2 - Prob. 68E Ch. 9.2 - Prob. 69E Ch. 9.2 - Prob. 70E Ch. 9.2 - Prob. 71E Ch. 9.2 - Prob. 72E Ch. 9.2 - Prob. 73E Ch. 9.2 - Prob. 74E Ch. 9.2 - Prob. 75E Ch. 9.2 - Prob. 76E Ch. 9.2 - Probability In Exercises 77 and 78, the random...Ch. 9.2 - Prob. 78E Ch. 9.2 - Probability A fair coin is tossed repeatedly. The...Ch. 9.2 - Prob. 80E Ch. 9.2 - Area The sides of a square are 16 inches in...Ch. 9.2 - Prob. 82E Ch. 9.2 - Prob. 83E Ch. 9.2 - Prob. 84E Ch. 9.2 - Prob. 85E Ch. 9.2 - Sphereflake The sphereflake shown below is a...Ch. 9.2 - Prob. 87E Ch. 9.2 - Prob. 88E Ch. 9.2 - Prob. 89E Ch. 9.2 - Prob. 90E Ch. 9.2 - Prob. 91E Ch. 9.2 - Prob. 92E Ch. 9.2 - Prob. 93E Ch. 9.2 - Prob. 94E Ch. 9.2 - Prob. 95E Ch. 9.2 - Prob. 96E Ch. 9.2 - Prob. 97E Ch. 9.2 - Proof Given two infinite series an and bn such...Ch. 9.2 - Prob. 99E Ch. 9.2 - Prob. 100E Ch. 9.2 - Prob. 101E Ch. 9.2 - Prob. 102E Ch. 9.2 - Prob. 103E Ch. 9.2 - Prob. 104E Ch. 9.3 - CONCEPT CHECK Integral Test What conditions have...Ch. 9.3 - Prob. 2E Ch. 9.3 - Prob. 3E Ch. 9.3 - Prob. 4E Ch. 9.3 - Prob. 5E Ch. 9.3 - Prob. 6E Ch. 9.3 - Using the Integral Test In Exercises 3-22, confirm...Ch. 9.3 - Using the Integral Test In Exercises 3-22, confirm...Ch. 9.3 - Using the Integral Test In Exercises 3-22, confirm...Ch. 9.3 - Prob. 10E Ch. 9.3 - Prob. 11E Ch. 9.3 - Prob. 12E Ch. 9.3 - Prob. 13E Ch. 9.3 - Using the Integral Test In Exercises 3-22, confirm...Ch. 9.3 - Using the Integral Test In Exercises 3-22, confirm...Ch. 9.3 - Prob. 16E Ch. 9.3 - Using the Integral Test In Exercises 3-22, confirm...Ch. 9.3 - Using the Integral Test In Exercises 3-22, confirm...Ch. 9.3 - Using the Integral Test In Exercises 3-22, confirm...Ch. 9.3 - Using the Integral Test In Exercises 3-22, confirm...Ch. 9.3 - Using the Integral Test In Exercises 3-22, confirm...Ch. 9.3 - Using the Integral Test In Exercises 3-22, confirm...Ch. 9.3 - Using the Integral Test In Exercises 23 and 24,...Ch. 9.3 - Using the Integral Test In Exercises 23 and 24,...Ch. 9.3 - Conditions of the Integral Test In Exercises 2528,...Ch. 9.3 - Conditions of the Integral Test In Exercises...Ch. 9.3 - Conditions of the Integral Test In Exercises...Ch. 9.3 - Conditions of the Integral Test In Exercises...Ch. 9.3 - Using the Integral Test In Exercises 29-32, use...Ch. 9.3 - Using the Integral Test In Exercises 29-32, use...Ch. 9.3 - Prob. 31E Ch. 9.3 - Prob. 32E Ch. 9.3 - Prob. 33E Ch. 9.3 - Using a p -Series In Exercises 33-38, use Theorem...Ch. 9.3 - Prob. 35E Ch. 9.3 - Prob. 36E Ch. 9.3 - Prob. 37E Ch. 9.3 - Prob. 38E Ch. 9.3 - Prob. 39E Ch. 9.3 - Prob. 40E Ch. 9.3 - Prob. 41E Ch. 9.3 - Prob. 42E Ch. 9.3 - Using a Series Use a graph to show that the...Ch. 9.3 - HOW DO YOU SEE IT? The graphs show the sequences...Ch. 9.3 - Finding Values In Exercises 45-50, find the...Ch. 9.3 - Finding Values In Exercises 45-50 Find the...Ch. 9.3 - Finding Values In Exercises 45-50, find the...Ch. 9.3 - Finding Values In Exercises 45-50, find the...Ch. 9.3 - Finding Values In Exercises 4550. find the...Ch. 9.3 - Finding Values In Exercises 45-50, find the...Ch. 9.3 - Proof Let f be a positive, continues, and...Ch. 9.3 - Using a Remainder Show that the results of...Ch. 9.3 - Approximating a Sum In Exercises 53-58, use the...Ch. 9.3 - Prob. 54E Ch. 9.3 - Prob. 55E Ch. 9.3 - Prob. 56E Ch. 9.3 - Prob. 57E Ch. 9.3 - Prob. 58E Ch. 9.3 - Finding a Value In Exercises 59-62, use the result...Ch. 9.3 - Prob. 60E Ch. 9.3 - Prob. 61E Ch. 9.3 - Finding a Value In Exercises 5962, use the result...Ch. 9.3 - Prob. 63E Ch. 9.3 - Prob. 64E Ch. 9.3 - Euler's Constant Let sn=k=1n1k=1+12+...+1n. (a)...Ch. 9.3 - Prob. 66E Ch. 9.3 - Prob. 67E Ch. 9.3 - Prob. 68E Ch. 9.3 - Prob. 69E Ch. 9.3 - Prob. 70E Ch. 9.3 - Prob. 71E Ch. 9.3 - Prob. 72E Ch. 9.3 - Prob. 73E Ch. 9.3 - Prob. 74E Ch. 9.3 - Prob. 75E Ch. 9.3 - Prob. 76E Ch. 9.3 - Prob. 77E Ch. 9.3 - Prob. 78E Ch. 9.3 - Prob. 79E Ch. 9.3 - Prob. 80E Ch. 9.4 - CONCEPT CHECK" Direct Comparison Test You want to...Ch. 9.4 - Prob. 2E Ch. 9.4 - Prob. 3E Ch. 9.4 - Prob. 4E Ch. 9.4 - Prob. 5E Ch. 9.4 - Prob. 6E Ch. 9.4 - Prob. 7E Ch. 9.4 - Prob. 8E Ch. 9.4 - Prob. 9E Ch. 9.4 - Using the Direct Comparison Test In Exercises...Ch. 9.4 - Prob. 11E Ch. 9.4 - Prob. 12E Ch. 9.4 - Prob. 13E Ch. 9.4 - Prob. 14E Ch. 9.4 - Prob. 15E Ch. 9.4 - Using the Direct Comparison Test In Exercises...Ch. 9.4 - Prob. 17E Ch. 9.4 - Using the Limit Comparison Test In Exercises...Ch. 9.4 - Using the Limit Comparison Test In Exercises...Ch. 9.4 - Using the Limit Comparison Test In Exercises...Ch. 9.4 - Using the Limit Comparison Test In Exercises...Ch. 9.4 - Using the Limit Comparison Test In Exercises...Ch. 9.4 - Using the Limit Comparison Test In Exercises...Ch. 9.4 - Using the Limit Comparison Test In Exercises...Ch. 9.4 - Using the Limit Comparison Test In Exercises...Ch. 9.4 - Using the Limit Comparison Test In Exercises...Ch. 9.4 - Determining Convergence or Divergence In Exercises...Ch. 9.4 - Determining Convergence or Divergence In Exercises...Ch. 9.4 - Determining Convergence or Divergence In Exercises...Ch. 9.4 - Determining Convergence or Divergence In Exercises...Ch. 9.4 - Determining Convergence or Divergence In Exercises...Ch. 9.4 - Determining Convergence or Divergence In Exercises...Ch. 9.4 - Determining Convergence or Divergence In Exercises...Ch. 9.4 - Determining Convergence or Divergence In Exercises...Ch. 9.4 - Using the Limit Comparison Test Use die Limit...Ch. 9.4 - Prob. 36E Ch. 9.4 - Prob. 37E Ch. 9.4 - Prob. 38E Ch. 9.4 - Prob. 39E Ch. 9.4 - Prob. 40E Ch. 9.4 - Prob. 41E Ch. 9.4 - Prob. 42E Ch. 9.4 - Determining Convergence or Divergence In Exercises...Ch. 9.4 - Determining Convergence or Divergence In Exercises...Ch. 9.4 - Prob. 45E Ch. 9.4 - Prob. 46E Ch. 9.4 - Prob. 47E Ch. 9.4 - Prob. 48E Ch. 9.4 - Prob. 49E Ch. 9.4 - Prob. 50E Ch. 9.4 - Prob. 51E Ch. 9.4 - Prob. 52E Ch. 9.4 - Prob. 53E Ch. 9.4 - Prob. 54E Ch. 9.4 - Prob. 55E Ch. 9.4 - Prob. 56E Ch. 9.4 - Prob. 57E Ch. 9.4 - Prob. 58E Ch. 9.4 - Proof Prove that if the nonnegative series...Ch. 9.4 - Prob. 60E Ch. 9.4 - Finding Series Find two series that demonstrate...Ch. 9.4 - Prob. 62E Ch. 9.4 - Prob. 63E Ch. 9.4 - Prob. 64E Ch. 9.4 - Prob. 65E Ch. 9.4 - Verifying Divergence Use the result of Exercise 64...Ch. 9.4 - Prob. 67E Ch. 9.4 - Prob. 68E Ch. 9.4 - Prob. 69E Ch. 9.4 - Prob. 70E Ch. 9.4 - Prob. 71E Ch. 9.4 - Prob. 72E Ch. 9.5 - CONCEPT CHECK Alternating Series An alternating...Ch. 9.5 - Prob. 2E Ch. 9.5 - Absolute and Conditional Convergence In your own...Ch. 9.5 - Prob. 4E Ch. 9.5 - Prob. 5E Ch. 9.5 - Numerical and Graphical Analysis In Exercises 5-8,...Ch. 9.5 - Numerical and Graphical Analysis In Exercises 5-8,...Ch. 9.5 - Numerical and Graphical Analysis In Exercises 5-8,...Ch. 9.5 - Determining Convergence or Divergence In Exercises...Ch. 9.5 - Determining Convergence or Divergence In Exercises...Ch. 9.5 - Determining Convergence or Divergence In Exercises...Ch. 9.5 - Determining Convergence or Divergence In Exercises...Ch. 9.5 - Determining Convergence or Divergence In Exercises...Ch. 9.5 - Determining Convergence or Divergence In Exercises...Ch. 9.5 - Determining Convergence or Divergence In Exercises...Ch. 9.5 - Determining Convergence or Divergence In Exercises...Ch. 9.5 - Determining Convergence or Divergence In Exercises...Ch. 9.5 - Determining Convergence or Divergence In Exercises...Ch. 9.5 - Determining Convergence or Divergence In Exercises...Ch. 9.5 - Determining Convergence or Divergence In Exercises...Ch. 9.5 - Determining Convergence or Divergence In Exercises...Ch. 9.5 - Determining Convergence or Divergence In Exercise...Ch. 9.5 - Determining Convergence or Divergence In Exercises...Ch. 9.5 - Determining Convergence or Divergence In Exercises...Ch. 9.5 - Determining Convergence or Divergence In Exercises...Ch. 9.5 - Determining Convergence or Divergence In Exercises...Ch. 9.5 - Determining Convergence or Divergence In Exercises...Ch. 9.5 - Prob. 28E Ch. 9.5 - Prob. 29E Ch. 9.5 - Determining Convergence or Divergence In Exercises...Ch. 9.5 - Approximating the Sum of an Alternating Series In...Ch. 9.5 - Approximating the Sum of an Alternating Series In...Ch. 9.5 - Prob. 33E Ch. 9.5 - Prob. 34E Ch. 9.5 - Prob. 35E Ch. 9.5 - Finding the Number of Terms In Exercises 35-40,...Ch. 9.5 - Finding the Number of Terms In Exercises 35-40,...Ch. 9.5 - Finding the Number of Terms In Exercises 35-40,...Ch. 9.5 - Finding the Number of Terms In Exercises 35-40,...Ch. 9.5 - Finding the Number of Terms In Exercises 35-40,...Ch. 9.5 - Determining Absolute and Conditional Convergence...Ch. 9.5 - Determining Absolute and Conditional Convergence...Ch. 9.5 - Determining Absolute and Conditional Convergence...Ch. 9.5 - Determining Absolute and Conditional Convergence...Ch. 9.5 - Determining Absolute end Conditional Convergence...Ch. 9.5 - Determining Absolute end Conditional Convergence...Ch. 9.5 - Determining Absolute end Conditional Convergence...Ch. 9.5 - Prob. 48E Ch. 9.5 - Determining Absolute end Conditional Convergence...Ch. 9.5 - Determining Absolute end Conditional Convergence...Ch. 9.5 - Determining Absolute end Conditional Convergence...Ch. 9.5 - Determining Absolute end Conditional Convergence...Ch. 9.5 - Determining Absolute end Conditional Convergence...Ch. 9.5 - Determining Absolute end Conditional Convergence...Ch. 9.5 - Determining Absolute end Conditional Convergence...Ch. 9.5 - Determining Absolute end Conditional Convergence...Ch. 9.5 - Prob. 57E Ch. 9.5 - Determining Absolute end Conditional Convergence...Ch. 9.5 - Prob. 59E Ch. 9.5 - Prob. 60E Ch. 9.5 - Prob. 61E Ch. 9.5 - HOW DO YOU SEE IT? The graphs of the sequences of...Ch. 9.5 - Prob. 63E Ch. 9.5 - Prob. 64E Ch. 9.5 - Proof Prove that if | an | converges, then an2...Ch. 9.5 - Prob. 66E Ch. 9.5 - Prob. 67E Ch. 9.5 - Finding Values Find all values of x for which the...Ch. 9.5 - Prob. 69E Ch. 9.5 - Prob. 70E Ch. 9.5 - Prob. 71E Ch. 9.5 - Prob. 72E Ch. 9.5 - Prob. 73E Ch. 9.5 - Prob. 74E Ch. 9.5 - Prob. 75E Ch. 9.5 - Prob. 76E Ch. 9.5 - Prob. 77E Ch. 9.5 - Prob. 78E Ch. 9.5 - Prob. 79E Ch. 9.5 - Prob. 80E Ch. 9.5 - Prob. 81E Ch. 9.5 - Prob. 82E Ch. 9.6 - CONCEPT CHECK Ratio and Root Tests In Exercises...Ch. 9.6 - Prob. 2E Ch. 9.6 - Prob. 3E Ch. 9.6 - Prob. 4E Ch. 9.6 - Prob. 5E Ch. 9.6 - Prob. 6E Ch. 9.6 - Prob. 7E Ch. 9.6 - Prob. 8E Ch. 9.6 - Prob. 9E Ch. 9.6 - Matching In Exercises 9-14, match the series with...Ch. 9.6 - Matching In Exercises 9-14, match the series with...Ch. 9.6 - Matching In Exercises 9-14, match the series with...Ch. 9.6 - Matching In Exercises 9-14, match the series with...Ch. 9.6 - Prob. 14E Ch. 9.6 - Numerical, Graphical, and Analytic Analysis In...Ch. 9.6 - Prob. 16E Ch. 9.6 - Prob. 17E Ch. 9.6 - Prob. 18E Ch. 9.6 - Prob. 19E Ch. 9.6 - Prob. 20E Ch. 9.6 - Prob. 21E Ch. 9.6 - Prob. 22E Ch. 9.6 - Prob. 23E Ch. 9.6 - Prob. 24E Ch. 9.6 - Prob. 25E Ch. 9.6 - Prob. 26E Ch. 9.6 - Prob. 27E Ch. 9.6 - Using the Ratio Test In Exercises 17-38, use the...Ch. 9.6 - Prob. 29E Ch. 9.6 - Prob. 30E Ch. 9.6 - Prob. 31E Ch. 9.6 - Prob. 32E Ch. 9.6 - Prob. 33E Ch. 9.6 - Prob. 34E Ch. 9.6 - Prob. 35E Ch. 9.6 - Prob. 36E Ch. 9.6 - Using the Ratio Test In Exercises 17-38, use the...Ch. 9.6 - Prob. 38E Ch. 9.6 - Prob. 39E Ch. 9.6 - Using the Root Test In Exercises 39-52, use the...Ch. 9.6 - Prob. 41E Ch. 9.6 - Prob. 42E Ch. 9.6 - Prob. 43E Ch. 9.6 - Prob. 44E Ch. 9.6 - Prob. 45E Ch. 9.6 - Using the Root Test In Exercises 39-52, use the...Ch. 9.6 - Using the Root Test In Exercises 39-52, use the...Ch. 9.6 - Using the Root Test In Exercises 39-52, use the...Ch. 9.6 - Prob. 49E Ch. 9.6 - Prob. 50E Ch. 9.6 - Prob. 51E Ch. 9.6 - Prob. 52E Ch. 9.6 - Prob. 53E Ch. 9.6 - Prob. 54E Ch. 9.6 - Prob. 55E Ch. 9.6 - Prob. 56E Ch. 9.6 - Prob. 57E Ch. 9.6 - Prob. 58E Ch. 9.6 - Prob. 59E Ch. 9.6 - Review In Exercises 53-70, determine the...Ch. 9.6 - Prob. 61E Ch. 9.6 - Prob. 62E Ch. 9.6 - Prob. 63E Ch. 9.6 - Prob. 64E Ch. 9.6 - Prob. 65E Ch. 9.6 - Prob. 66E Ch. 9.6 - Prob. 67E Ch. 9.6 - Prob. 68E Ch. 9.6 - Prob. 69E Ch. 9.6 - Prob. 70E Ch. 9.6 - Prob. 71E Ch. 9.6 - Prob. 72E Ch. 9.6 - Prob. 73E Ch. 9.6 - Prob. 74E Ch. 9.6 - Prob. 75E Ch. 9.6 - Prob. 76E Ch. 9.6 - Prob. 77E Ch. 9.6 - Prob. 78E Ch. 9.6 - Prob. 79E Ch. 9.6 - Prob. 80E Ch. 9.6 - Prob. 81E Ch. 9.6 - Prob. 82E Ch. 9.6 - Prob. 83E Ch. 9.6 - Prob. 84E Ch. 9.6 - Prob. 85E Ch. 9.6 - Prob. 86E Ch. 9.6 - Prob. 87E Ch. 9.6 - Prob. 88E Ch. 9.6 - Prob. 89E Ch. 9.6 - Prob. 90E Ch. 9.6 - Prob. 91E Ch. 9.6 - Prob. 92E Ch. 9.6 - Prob. 93E Ch. 9.6 - Prob. 94E Ch. 9.6 - Prob. 95E Ch. 9.6 - Prob. 96E Ch. 9.6 - Prob. 97E Ch. 9.6 - Prob. 98E Ch. 9.6 - Prob. 99E Ch. 9.6 - Prob. 100E Ch. 9.6 - Prob. 101E Ch. 9.6 - Prob. 102E Ch. 9.6 - Prob. 103E Ch. 9.6 - Prob. 104E Ch. 9.6 - Prob. 105E Ch. 9.6 - Prob. 106E Ch. 9.6 - Prob. 107E Ch. 9.6 - Prob. 108E Ch. 9.7 - CONCEPT CHECK Polynomial Approximation An...Ch. 9.7 - Prob. 2E Ch. 9.7 - Prob. 3E Ch. 9.7 - Prob. 4E Ch. 9.7 - Matching In Exercises 5-8, match the Taylor...Ch. 9.7 - Matching In Exercises 5-8, match the Taylor...Ch. 9.7 - Prob. 7E Ch. 9.7 - Matching In Exercises 5-8, match the Taylor...Ch. 9.7 - Finding a First-Degree Polynomial Approximation In...Ch. 9.7 - Finding a First-Degree Polynomial Approximation In...Ch. 9.7 - Prob. 11E Ch. 9.7 - Prob. 12E Ch. 9.7 - Prob. 13E Ch. 9.7 - Prob. 14E Ch. 9.7 - Conjecture Consider the function f(x)=cosx and its...Ch. 9.7 - Conjecture Consider the function f(x)=x2ex. (a)...Ch. 9.7 - Prob. 17E Ch. 9.7 - Prob. 18E Ch. 9.7 - Prob. 19E Ch. 9.7 - Prob. 20E Ch. 9.7 - Prob. 21E Ch. 9.7 - Prob. 22E Ch. 9.7 - Prob. 23E Ch. 9.7 - Prob. 24E Ch. 9.7 - Prob. 25E Ch. 9.7 - Prob. 26E Ch. 9.7 - Finding a Taylor Polynomial In Exercises 27-32,...Ch. 9.7 - Finding a Taylor Polynomial In Exercises 27-32,...Ch. 9.7 - Finding a Taylor Polynomial In Exercises 27-32,...Ch. 9.7 - Prob. 30E Ch. 9.7 - Prob. 31E Ch. 9.7 - Prob. 32E Ch. 9.7 - Prob. 33E Ch. 9.7 - Prob. 34E Ch. 9.7 - Prob. 35E Ch. 9.7 - Prob. 36E Ch. 9.7 - Prob. 37E Ch. 9.7 - Prob. 38E Ch. 9.7 - Prob. 39E Ch. 9.7 - Prob. 40E Ch. 9.7 - Prob. 41E Ch. 9.7 - Prob. 42E Ch. 9.7 - Prob. 43E Ch. 9.7 - Prob. 44E Ch. 9.7 - Using Taylors Theorem In Exercises 45-50, use...Ch. 9.7 - Prob. 46E Ch. 9.7 - Using Taylors Theorem In Exercises 45-50, use...Ch. 9.7 - Prob. 48E Ch. 9.7 - Using Taylors Theorem In Exercises 45-50, use...Ch. 9.7 - Using Taylors Theorem In Exercises 45-50, use...Ch. 9.7 - Prob. 51E Ch. 9.7 - Prob. 52E Ch. 9.7 - Prob. 53E Ch. 9.7 - Prob. 54E Ch. 9.7 - Prob. 55E Ch. 9.7 - Prob. 56E Ch. 9.7 - Prob. 57E Ch. 9.7 - Prob. 58E Ch. 9.7 - Finding Values In Exercises 59-62, determine the...Ch. 9.7 - Finding Values In Exercises 59-62, determine the...Ch. 9.7 - Finding Values In Exercises 59-62, determine the...Ch. 9.7 - Prob. 62E Ch. 9.7 - Prob. 63E Ch. 9.7 - Prob. 64E Ch. 9.7 - Prob. 65E Ch. 9.7 - Prob. 66E Ch. 9.7 - Prob. 67E Ch. 9.7 - Differentiating Maclaurin Polynomials (a)...Ch. 9.7 - Prob. 69E Ch. 9.7 - Prob. 70E Ch. 9.7 - Prob. 71E Ch. 9.7 - Prob. 72E Ch. 9.7 - Prob. 73E Ch. 9.8 - Prob. 1E Ch. 9.8 - Prob. 2E Ch. 9.8 - Prob. 3E Ch. 9.8 - Prob. 4E Ch. 9.8 - Finding the Center of a Power Series In Exercises...Ch. 9.8 - Finding the Center of a Power Series In Exercises...Ch. 9.8 - Finding the Center of a Power Series In Exercises...Ch. 9.8 - Finding the Center of a Power Series In Exercises...Ch. 9.8 - Finding the Radius of Convergence In Exercises...Ch. 9.8 - Finding the Radius of Convergence In Exercises...Ch. 9.8 - Finding the Radius of Convergence In Exercise...Ch. 9.8 - Finding the Radius of Convergence In Exercises...Ch. 9.8 - Finding the Radius of Convergence In Exercises...Ch. 9.8 - Finding the Radius of Convergence In Exercises...Ch. 9.8 - Finding the Interval of Convergence In Exercises...Ch. 9.8 - Finding the Interval of Convergence In Exercises...Ch. 9.8 - Finding the Interval of Convergence In Exercises...Ch. 9.8 - Finding the Interval of Convergence In Exercises...Ch. 9.8 - Finding the Interval of Convergence In Exercises...Ch. 9.8 - Finding the Interval of Convergence In Exercises...Ch. 9.8 - Finding the Interval of Convergence In Exercises...Ch. 9.8 - Finding the Interval of Convergence In Exercises...Ch. 9.8 - Finding the Interval of Convergence In Exercises...Ch. 9.8 - Finding the Interval of Convergence In Exercise...Ch. 9.8 - Finding the Interval of Convergence In Exercise...Ch. 9.8 - Finding the Interval of Convergence In Exercise...Ch. 9.8 - Finding the Interval of Convergence In Exercise...Ch. 9.8 - Finding the Interval of Convergence In Exercise...Ch. 9.8 - Finding the Interval of Convergence In Exercise...Ch. 9.8 - Finding the Interval of Convergence In Exercises...Ch. 9.8 - Finding the Interval of Convergence In Exercises...Ch. 9.8 - Finding the Interval of Convergence In Exercise...Ch. 9.8 - Finding the Interval of Convergence In Exercise...Ch. 9.8 - Finding the Interval of Convergence In Exercise...Ch. 9.8 - Finding the Interval of Convergence In Exercises...Ch. 9.8 - Finding the Interval of Convergence In Exercises...Ch. 9.8 - Finding the Interval of Convergence In Exercise...Ch. 9.8 - Finding the Interval of Convergence In Exercises...Ch. 9.8 - Finding the Radius of Convergence In Exercises 39...Ch. 9.8 - Finding the Radius of Convergence In Exercises 39...Ch. 9.8 - Finding the Interval of Convergence In Exercises...Ch. 9.8 - Finding the Interval of Convergence In Exercises...Ch. 9.8 - Prob. 43E Ch. 9.8 - Finding the Interval of Convergence In Exercises...Ch. 9.8 - Writing an Equivalent Series In Exercises 45-48,...Ch. 9.8 - Writing an Equivalent Series In Exercises 45-48,...Ch. 9.8 - Prob. 47E Ch. 9.8 - Prob. 48E Ch. 9.8 - Prob. 49E Ch. 9.8 - Finding Intervals of Convergence In Exercises...Ch. 9.8 - Prob. 51E Ch. 9.8 - Prob. 52E Ch. 9.8 - Prob. 53E Ch. 9.8 - Prob. 54E Ch. 9.8 - Prob. 55E Ch. 9.8 - Prob. 56E Ch. 9.8 - Using Power Series Let...Ch. 9.8 - Prob. 58E Ch. 9.8 - Prob. 59E Ch. 9.8 - Prob. 60E Ch. 9.8 - Prob. 61E Ch. 9.8 - Differential Equation In Exercises 59-64, show...Ch. 9.8 - Prob. 63E Ch. 9.8 - Prob. 64E Ch. 9.8 - Bessel Function The Bessel function of order 0 is...Ch. 9.8 - Prob. 66E Ch. 9.8 - Prob. 67E Ch. 9.8 - Investigation The interval of convergence of the...Ch. 9.8 - Prob. 69E Ch. 9.8 - Prob. 70E Ch. 9.8 - Identifying a Function In Exercises 69-72, the...Ch. 9.8 - Prob. 72E Ch. 9.8 - Prob. 73E Ch. 9.8 - Prob. 74E Ch. 9.8 - Prob. 75E Ch. 9.8 - Prob. 76E Ch. 9.8 - Proof Prove that the power series...Ch. 9.8 - Using a Power Series Let g(x)=1+2x+x2+2x3+x4+...Ch. 9.8 - Prob. 79E Ch. 9.8 - Proof Prove that if the power series n=0cnxn has a...Ch. 9.8 - Prob. 81E Ch. 9.9 - Prob. 1E Ch. 9.9 - Prob. 2E Ch. 9.9 - Finding a Geometric Power Series In Exercises 3-6,...Ch. 9.9 - Finding a Geometric Power Series In Exercises 3-6,...Ch. 9.9 - Finding a Geometric Power Series In Exercises 3-6,...Ch. 9.9 - Finding a Geometric Power Series In Exercises 3-6,...Ch. 9.9 - Finding a Power Series In Exercises 7-18, find a...Ch. 9.9 - Finding a Power Series In Exercises 7-18, find a...Ch. 9.9 - Finding a Power Series In Exercises 7-18, find a...Ch. 9.9 - Finding a Power Series In Exercises 7-18, find a...Ch. 9.9 - Finding a Power Series In Exercises 7-18, find a...Ch. 9.9 - Finding a Power Series In Exercises 7-18, find a...Ch. 9.9 - Prob. 13E Ch. 9.9 - Finding a Power Series In Exercises 7-18, find a...Ch. 9.9 - Finding a Power Series In Exercises 7-18, find a...Ch. 9.9 - Finding a Power Series In Exercises 7-18, find a...Ch. 9.9 - Prob. 17E Ch. 9.9 - Finding a Power Series In Exercises 7-18, find a...Ch. 9.9 - Prob. 19E Ch. 9.9 - Prob. 20E Ch. 9.9 - Prob. 21E Ch. 9.9 - Prob. 22E Ch. 9.9 - Using a Power Series In Exercises 19-28, use the...Ch. 9.9 - Using a Power Series In Exercises 19-28, use the...Ch. 9.9 - Prob. 25E Ch. 9.9 - Prob. 26E Ch. 9.9 - Prob. 27E Ch. 9.9 - Prob. 28E Ch. 9.9 - Prob. 29E Ch. 9.9 - Prob. 30E Ch. 9.9 - Prob. 31E Ch. 9.9 - Prob. 32E Ch. 9.9 - Prob. 33E Ch. 9.9 - Prob. 34E Ch. 9.9 - Prob. 35E Ch. 9.9 - Prob. 36E Ch. 9.9 - Prob. 37E Ch. 9.9 - Using a Power Series In Exercises 37-40, use the...Ch. 9.9 - Prob. 39E Ch. 9.9 - Prob. 40E Ch. 9.9 - Prob. 41E Ch. 9.9 - Prob. 42E Ch. 9.9 - Prob. 43E Ch. 9.9 - Prob. 44E Ch. 9.9 - Prob. 45E Ch. 9.9 - Prob. 46E Ch. 9.9 - Prob. 47E Ch. 9.9 - Prob. 48E Ch. 9.9 - Prob. 49E Ch. 9.9 - Prob. 50E Ch. 9.9 - Prob. 51E Ch. 9.9 - Prob. 52E Ch. 9.9 - Prob. 53E Ch. 9.9 - Prob. 54E Ch. 9.9 - Prob. 55E Ch. 9.9 - Prob. 56E Ch. 9.9 - Prob. 57E Ch. 9.10 - Prob. 1E Ch. 9.10 - Prob. 2E Ch. 9.10 - Prob. 3E Ch. 9.10 - Finding a Taylor Series Explain how to use the...Ch. 9.10 - Finding a Taylor Series In Exercises 5-16, use the...Ch. 9.10 - Finding a Taylor Series In Exercises 5-16, use the...Ch. 9.10 - Finding a Taylor Series In Exercises 5-16, use the...Ch. 9.10 - Finding a Taylor Series In Exercises 5-16, use the...Ch. 9.10 - Finding a Taylor Series In Exercises 5-16, use the...Ch. 9.10 - Finding a Taylor Series In Exercises 5-16, use the...Ch. 9.10 - Finding a Taylor Series In Exercises 5-16, use the...Ch. 9.10 - Finding a Taylor Series In Exercises 5-16, use the...Ch. 9.10 - Prob. 13E Ch. 9.10 - Finding a Taylor Series In Exercises 5-16, use the...Ch. 9.10 - Prob. 15E Ch. 9.10 - Finding a Taylor Series In Exercises 5-16, use the...Ch. 9.10 - Prob. 17E Ch. 9.10 - Prob. 18E Ch. 9.10 - Prob. 19E Ch. 9.10 - Prob. 20E Ch. 9.10 - Prob. 21E Ch. 9.10 - Prob. 22E Ch. 9.10 - Using a Binomial Series In Exercises 21-26, use...Ch. 9.10 - Prob. 24E Ch. 9.10 - Prob. 25E Ch. 9.10 - Prob. 26E Ch. 9.10 - Finding a Maclaurin Series In Exercises 27-40,...Ch. 9.10 - Prob. 28E Ch. 9.10 - Prob. 29E Ch. 9.10 - Prob. 30E Ch. 9.10 - Prob. 31E Ch. 9.10 - Prob. 32E Ch. 9.10 - Prob. 33E Ch. 9.10 - Prob. 34E Ch. 9.10 - Prob. 35E Ch. 9.10 - Prob. 36E Ch. 9.10 - Finding a Maclaurin Series In Exercises 27-40,...Ch. 9.10 - Finding a Maclaurin Series In Exercises 27-40,...Ch. 9.10 - Prob. 39E Ch. 9.10 - Prob. 40E Ch. 9.10 - Prob. 41E Ch. 9.10 - Prob. 42E Ch. 9.10 - Prob. 43E Ch. 9.10 - Prob. 44E Ch. 9.10 - Prob. 45E Ch. 9.10 - Prob. 46E Ch. 9.10 - Prob. 47E Ch. 9.10 - Prob. 48E Ch. 9.10 - Prob. 49E Ch. 9.10 - Prob. 50E Ch. 9.10 - Prob. 51E Ch. 9.10 - Prob. 52E Ch. 9.10 - Prob. 53E Ch. 9.10 - Prob. 54E Ch. 9.10 - Prob. 55E Ch. 9.10 - Prob. 56E Ch. 9.10 - Prob. 57E Ch. 9.10 - Prob. 58E Ch. 9.10 - Finding a Limit In Exercises 59-62, use the series...Ch. 9.10 - Prob. 60E Ch. 9.10 - Prob. 61E Ch. 9.10 - Prob. 62E Ch. 9.10 - Prob. 63E Ch. 9.10 - Prob. 64E Ch. 9.10 - Approximating an Integral In Exercises 63-70, use...Ch. 9.10 - Prob. 66E Ch. 9.10 - Prob. 67E Ch. 9.10 - Prob. 68E Ch. 9.10 - Prob. 69E Ch. 9.10 - Prob. 70E Ch. 9.10 - Prob. 71E Ch. 9.10 - Prob. 72E Ch. 9.10 - Prob. 73E Ch. 9.10 - Prob. 74E Ch. 9.10 - Prob. 75E Ch. 9.10 - Prob. 76E Ch. 9.10 - Prob. 77E Ch. 9.10 - Prob. 78E Ch. 9.10 - Projectile Motion A projectile fired from the...Ch. 9.10 - Prob. 80E Ch. 9.10 - Prob. 81E Ch. 9.10 - Prob. 82E Ch. 9.10 - Prob. 83E Ch. 9.10 - Prob. 84E Ch. 9.10 - Prob. 85E Ch. 9.10 - Prob. 86E Ch. 9.10 - Prob. 87E Ch. 9.10 - Prob. 88E Ch. 9.10 - Prob. 89E Ch. 9.10 - Prob. 90E Ch. 9.10 - Prob. 91E Ch. 9.10 - Using Fibonacci Numbers Show that the Maclaurin...Ch. 9.10 - Prob. 93E Ch. 9 - Writing the Terms of a Sequence In Exercises 1-4,...Ch. 9 - Prob. 2RE Ch. 9 - Prob. 3RE Ch. 9 - Prob. 4RE Ch. 9 - Prob. 5RE Ch. 9 - Prob. 6RE Ch. 9 - Prob. 7RE Ch. 9 - Prob. 8RE Ch. 9 - Prob. 9RE Ch. 9 - Prob. 10RE Ch. 9 - Prob. 11RE Ch. 9 - Prob. 12RE Ch. 9 - Prob. 13RE Ch. 9 - Prob. 14RE Ch. 9 - Prob. 15RE Ch. 9 - Determining Convergence or Divergence In Exercises...Ch. 9 - Prob. 17RE Ch. 9 - Prob. 18RE Ch. 9 - Prob. 19RE Ch. 9 - Prob. 20RE Ch. 9 - Prob. 21RE Ch. 9 - Prob. 22RE Ch. 9 - Prob. 23RE Ch. 9 - Prob. 24RE Ch. 9 - Prob. 25RE Ch. 9 - Prob. 26RE Ch. 9 - Prob. 27RE Ch. 9 - Finding Partial Sums In Exercises 27 and 28, find...Ch. 9 - Prob. 29RE Ch. 9 - Prob. 30RE Ch. 9 - Prob. 31RE Ch. 9 - Prob. 32RE Ch. 9 - Prob. 33RE Ch. 9 - Prob. 34RE Ch. 9 - Prob. 35RE Ch. 9 - Prob. 36RE Ch. 9 - Prob. 37RE Ch. 9 - Prob. 38RE Ch. 9 - Prob. 39RE Ch. 9 - Prob. 40RE Ch. 9 - Prob. 41RE Ch. 9 - Prob. 42RE Ch. 9 - Prob. 43RE Ch. 9 - Prob. 44RE Ch. 9 - Prob. 45RE Ch. 9 - Prob. 46RE Ch. 9 - Prob. 47RE Ch. 9 - Prob. 48RE Ch. 9 - Prob. 49RE Ch. 9 - Prob. 50RE Ch. 9 - Prob. 51RE Ch. 9 - Prob. 52RE Ch. 9 - Prob. 53RE Ch. 9 - Prob. 54RE Ch. 9 - Prob. 55RE Ch. 9 - Prob. 56RE Ch. 9 - Prob. 57RE Ch. 9 - Prob. 58RE Ch. 9 - Prob. 59RE Ch. 9 - Prob. 60RE Ch. 9 - Prob. 61RE Ch. 9 - Prob. 62RE Ch. 9 - Prob. 63RE Ch. 9 - Prob. 64RE Ch. 9 - Prob. 65RE Ch. 9 - Prob. 66RE Ch. 9 - Prob. 67RE Ch. 9 - Prob. 68RE Ch. 9 - Prob. 69RE Ch. 9 - Prob. 70RE Ch. 9 - Prob. 71RE Ch. 9 - Prob. 72RE Ch. 9 - Prob. 73RE Ch. 9 - Prob. 74RE Ch. 9 - Prob. 75RE Ch. 9 - Prob. 76RE Ch. 9 - Prob. 77RE Ch. 9 - Prob. 78RE Ch. 9 - Prob. 79RE Ch. 9 - Prob. 80RE Ch. 9 - Prob. 81RE Ch. 9 - Prob. 82RE Ch. 9 - Prob. 83RE Ch. 9 - Prob. 84RE Ch. 9 - Prob. 85RE Ch. 9 - Prob. 86RE Ch. 9 - Prob. 87RE Ch. 9 - Prob. 88RE Ch. 9 - Prob. 89RE Ch. 9 - Finding Intervals of Convergence In Exercises 89...Ch. 9 - Prob. 91RE Ch. 9 - Prob. 92RE Ch. 9 - Finding a Geometric Power Series In Exercises 93...Ch. 9 - Prob. 94RE Ch. 9 - Prob. 95RE Ch. 9 - Prob. 96RE Ch. 9 - Prob. 97RE Ch. 9 - Prob. 98RE Ch. 9 - Prob. 99RE Ch. 9 - Prob. 100RE Ch. 9 - Prob. 101RE Ch. 9 - Prob. 102RE Ch. 9 - Finding a Taylor Series In Exercises 103-110, use...Ch. 9 - Finding a Taylor Series In Exercises 103-110, use...Ch. 9 - Prob. 105RE Ch. 9 - Prob. 106RE Ch. 9 - Prob. 107RE Ch. 9 - Prob. 108RE Ch. 9 - Finding a Taylor SeriesIn Exercises 103-110, use...Ch. 9 - Prob. 110RE Ch. 9 - Prob. 111RE Ch. 9 - Prob. 112RE Ch. 9 - Prob. 113RE Ch. 9 - Prob. 114RE Ch. 9 - Prob. 115RE Ch. 9 - Prob. 116RE Ch. 9 - Prob. 117RE Ch. 9 - Prob. 118RE Ch. 9 - Prob. 1PS Ch. 9 - Prob. 2PS Ch. 9 - Prob. 3PS Ch. 9 - Finding a Limit Let T be an equilateral triangle...Ch. 9 - Prob. 5PS Ch. 9 - Prob. 6PS Ch. 9 - Prob. 7PS Ch. 9 - Prob. 8PS Ch. 9 - Prob. 9PS Ch. 9 - Prob. 10PS Ch. 9 - Prob. 11PS Ch. 9 - Prob. 12PS Ch. 9 - Prob. 13PS Ch. 9 - Prob. 14PS Ch. 9 - Prob. 15PS Ch. 9 - Prob. 16PS

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The Fibonacci sequence fn=1,1,2,3,5,8,13,21,... is defined recursively by f1=1,f2=1,fn+2=fn+1+fn for n=1,2,3,... a. Prove f1+f2+...+fn=fn+21 for all positive integers n. b. Use complete induction to prove that fn2n for all positive integers n. c. Use complete induction to prove that fn is given by the explicit formula fn=(1+5)n(15)n2n5 (This equation is known as Binet's formula, named after the 19th-century French mathematician Jacques Binet.)
Sum of a Finite Arithmetic Sequence Find the sum of the integers from 30 to 80.
Fibonaccis RabbitsFibonacci posed the following problem: Suppose that rabbits live forever and that every month each pair produces a new pair that becomes productive at age 2 months. If we start with one newborn pair, how many pairs of rabbits will we have in the n th month? Show that the answer if Fn, where Fn is the n th term of the Fibonacci sequence.

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