Explanation Given: The series is ∑ k = 1 ∞ 1 sin h k . Result used: (1) Let ∑ a k and ∑ b k are the series with positive terms and lim x → ∞ a n b n = L , where L is a finite number. (i) If 0 < L < ∞ , then either both series ∑ a k and ∑ b k converges or both diverges. (ii) If L = 0 and ∑ b k converges, then ∑ a k converges. (iii) If L = ∞ and ∑ b k diverges, then ∑ a k diverges” (2) The p -series ∑ k = 0 ∞ a r k converges if | r | < 1 and diverges if | r | ≤ 1 . Calculation: Consider the series ∑ k = 1 ∞ 1 sin h k . 1 sin h k = 2 e k − e − k 2 e k − e − k < 1 e k Consider the series ∑ k = 1 ∞ b k = ∑ k = 1 ∞ 1 e k , which must be greater than. ∑ k = 1 ∞ a k = ∑ k = 1 ∞ 1 sin h k

Calculus: Early Transcendentals (2nd Edition)

2nd Edition

ISBN: 9780321947345

Author: William L. Briggs, Lyle Cochran, Bernard Gillett

Publisher: PEARSON

See similar textbooks

Videos

Question

Chapter 8, Problem 40RE

To determine

Whether the series ∑k=1∞1sinhk converges or diverges.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 8, Problem 39RE

Chapter 8, Problem 41RE

Students have asked these similar questions

find value of p to make convergent

Test for convergence/Divergence

Determine weather the series is convergent or divergent. Write the exact test that you used.

Chapter 8 Solutions

Calculus: Early Transcendentals (2nd Edition)

Ch. 8.1 - Define sequence and give an example.Ch. 8.1 - Suppose the sequence {an} is defined by the...Ch. 8.1 - Suppose the sequence {an} is defined by the...Ch. 8.1 - Prob. 4E Ch. 8.1 - Prob. 5E Ch. 8.1 - Given the series k=1k, evaluate the first four...Ch. 8.1 - The terms of a sequence of partial sums are...Ch. 8.1 - Consider the infinite series k=11k. Evaluate the...Ch. 8.1 - Explicit formulas Write the first four terms of...Ch. 8.1 - Explicit formulas Write the first four terms of...

Additional Math Textbook Solutions

Find more solutions based on key concepts

Consider an experiment that consists of determining the type of job-either blue collar or white collar-and the ...

A First Course in Probability (10th Edition)

Fill in each blanks so that the resulting statement is true. Any set of ordered pairs is called a/an _______. T...

College Algebra (7th Edition)

CHECK POINT 1 Write a word description of the set L = {a, b, c, d, e, f}.

Thinking Mathematically (6th Edition)

Whether the requirements for a hypothesis test are satisfied or not.

Elementary Statistics

x vs. Two symbols are used for the mean: and x. a. Which represents a parameter, and which a statistic? b. In...

Introductory Statistics

In Exercises 9-12, assume that 50 births are randomly selected. Use subjective judgment to describe the given n...

Elementary Statistics (13th Edition)

Knowledge Booster

$Calculus$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

Whether the series ∑ k = 1 ∞ 1 sin h k converges or diverges.

Solution Summary: The author analyzes whether the series displaystyle 'underset' converges or diverges.

Videos

Whether the series ∑k=1∞1sinhk converges or diverges.

Want to see the full answer?

Chapter 8 Solutions

Additional Math Textbook Solutions