Mathematical Methods in the Physical Sciences
Mathematical Methods in the Physical Sciences
3rd Edition
ISBN: 9780471198260
Author: Mary L. Boas
Publisher: Wiley, John & Sons, Incorporated
bartleby

Concept explainers

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.
bartleby

Videos

Textbook Question
Book Icon
Chapter 1.2, Problem 9P

In the following problems, find the limit of the given sequence as n   →   ∞ .

n ​   sin ( 1 / n )

Expert Solution & Answer
Check Mark

Want to see the full answer?

Check out a sample textbook solution
Blurred answer
Previous
Chapter 1.2, Problem 8P
Next
Chapter 1.4, Problem 1P
Students have asked these similar questions
Find the limit of the following sequence. Please show steps
Q9
(cos n) Find the limit of the sequence dn 6Th

Chapter 1 Solutions

Mathematical Methods in the Physical Sciences

Ch. 1.1 - In the bouncing ball example above, find the...Ch. 1.1 - Derive the formula (1.4) for the sum Sn of the...Ch. 1.1 - Use equation (1.8) to find the fractions that are...Ch. 1.1 - Use equation (1.8) to find the fractions that are...Ch. 1.1 - Use equation (1.8) to find the fractions that are...Ch. 1.1 - Use equation (1.8) to find the fractions that are...Ch. 1.1 - Use equation (1.8) to find the fractions that are...Ch. 1.1 - Use equation (1.8) to find the fractions that are...Ch. 1.1 - Use equation (1.8) to find the fractions that are...Ch. 1.1 - Use equation (1.8) to find the fractions that are...
Ch. 1.1 - Use equation (1.8) to find the fractions that are...Ch. 1.1 - In a water purification process, one-nth of the...Ch. 1.1 - If you invest a dollar at 6% interest compounded...Ch. 1.1 - A computer program gives the result 1/6 for the...Ch. 1.1 - Connect the midpoints of the sides of an...Ch. 1.1 - Suppose a large number of particles are bouncing...Ch. 1.2 - In the following problems, find the limit of the...Ch. 1.2 - In the following problems, find the limit of the...Ch. 1.2 - In the following problems, find the limit of the...Ch. 1.2 - In the following problems, find the limit of the...Ch. 1.2 - In the following problems, find the limit of the...Ch. 1.2 - In the following problems, find the limit of the...Ch. 1.2 - In the following problems, find the limit of the...Ch. 1.2 - In the following problems, find the limit of the...Ch. 1.2 - In the following problems, find the limit of the...Ch. 1.4 - For the following series, write formulas for the...Ch. 1.4 - For the following, write formulas for the...Ch. 1.4 - For the following series, write formulas for the...Ch. 1.4 - For the following series, write formulas for the...Ch. 1.4 - For the following series, write formulas for the...Ch. 1.4 - For the following series, write formulas for the...Ch. 1.4 - For the following series, write formulas for the...Ch. 1.5 - Use the preliminary test to decide whether the...Ch. 1.5 - Use the preliminary test to decide whether the...Ch. 1.5 - Use the preliminary test to decide whether the...Ch. 1.5 - Use the preliminary test to decide whether the...Ch. 1.5 - Use the preliminary test to decide whether the...Ch. 1.5 - Use the preliminary test to decide whether the...Ch. 1.5 - Use the preliminary test to decide whether the...Ch. 1.5 - Use the preliminary test to decide whether the...Ch. 1.5 - Use the preliminary test to decide whether the...Ch. 1.5 - Use the preliminary test to decide whether the...Ch. 1.5 - Using (4.6), give a proof of the preliminary test....Ch. 1.6 - Show that n! 2 for all n 3. Hint: Write out a...Ch. 1.6 - Prove that the harmonic series n=11/n is divergent...Ch. 1.6 - Prove the convergence n=11/n2 by grouping terms...Ch. 1.6 - Use the comparison test to prove the convergence...Ch. 1.6 - Test the following series for convergence using...Ch. 1.6 - There are 9 one-digit numbers (1 to 9), 90...Ch. 1.6 - Use the integral test to find whether the...Ch. 1.6 - Use the integral test to find whether the...Ch. 1.6 - Use the integral test to find whether the...Ch. 1.6 - Use the integral test to find whether the...Ch. 1.6 - Use the integral test to find whether the...Ch. 1.6 - Use the integral test to find whether the...Ch. 1.6 - Use the integral test to find whether the...Ch. 1.6 - Use the integral test to find whether the...Ch. 1.6 - Use the integral test to prove the following...Ch. 1.6 - In testing 1/n2 for convergence, a student...Ch. 1.6 - Use the integral test to show that n=0en2...Ch. 1.6 - Use the ratio test to find whether the following...Ch. 1.6 - Use the ratio test to find whether the following...Ch. 1.6 - Use the ratio test to find whether the following...Ch. 1.6 - Use the ratio test to find whether the following...Ch. 1.6 - Use the ratio test to find whether the following...Ch. 1.6 - Use the ratio test to find whether the following...Ch. 1.6 - Use the ratio test to find whether the following...Ch. 1.6 - Use the ratio test to find whether the following...Ch. 1.6 - Use the ratio test to find whether the following...Ch. 1.6 - Use the ratio test to find whether the following...Ch. 1.6 - Use the ratio test to find whether the following...Ch. 1.6 - Use the ratio test to find whether the following...Ch. 1.6 - Prove the ratio test. Hint: If an+1/an1, take ...Ch. 1.6 - Use the special comparison test to find whether...Ch. 1.6 - Use the special comparison test to find whether...Ch. 1.6 - Use the special comparison test to find whether...Ch. 1.6 - Use the special comparison test to find whether...Ch. 1.6 - Use the special comparison test to find whether...Ch. 1.6 - Use the special comparison test to find whether...Ch. 1.6 - Prove the special comparison test. Hint (part a):...Ch. 1.7 - Test the following series for convergence....Ch. 1.7 - Test the following series for convergence....Ch. 1.7 - Test the following series for convergence....Ch. 1.7 - Test the following series for convergence....Ch. 1.7 - Test the following series for convergence....Ch. 1.7 - Test the following series for convergence....Ch. 1.7 - Test the following series for convergence....Ch. 1.7 - Test the following series for convergence....Ch. 1.7 - Prove that an absolutely convergent series n=1an...Ch. 1.7 - The following alternating series are divergent...Ch. 1.9 - Test the following series for convergence or...Ch. 1.9 - Test the following series for convergence or...Ch. 1.9 - Test the following series for convergence or...Ch. 1.9 - Test the following series for convergence or...Ch. 1.9 - Test the following series for convergence or...Ch. 1.9 - Test the following series for convergence or...Ch. 1.9 - Test the following series for convergence or...Ch. 1.9 - Test the following series for convergence or...Ch. 1.9 - Test the following series for convergence or...Ch. 1.9 - Test the following series for convergence or...Ch. 1.9 - Test the following series for convergence or...Ch. 1.9 - Test the following series for convergence or...Ch. 1.9 - Test the following series for convergence or...Ch. 1.9 - Test the following series for convergence or...Ch. 1.9 - Test the following series for convergence or...Ch. 1.9 - Test the following series for convergence or...Ch. 1.9 - Test the following series for convergence or...Ch. 1.9 - Test the following series for convergence or...Ch. 1.9 - Test the following series for convergence or...Ch. 1.9 - Test the following series for convergence or...Ch. 1.9 - Test the following series for convergence or...Ch. 1.9 - Test the following series for convergence or...Ch. 1.10 - Find the interval of convergence of each of the...Ch. 1.10 - Find the interval of convergence of each of the...Ch. 1.10 - Find the interval of convergence of each of the...Ch. 1.10 - Find the interval of convergence of each of the...Ch. 1.10 - Find the interval of convergence of each of the...Ch. 1.10 - Find the interval of convergence of each of the...Ch. 1.10 - Find the interval of convergence of each of the...Ch. 1.10 - Find the interval of convergence of each of the...Ch. 1.10 - Find the interval of convergence of each of the...Ch. 1.10 - Find the interval of convergence of each of the...Ch. 1.10 - Find the interval of convergence of each of the...Ch. 1.10 - Find the interval of convergence of each of the...Ch. 1.10 - Find the interval of convergence of each of the...Ch. 1.10 - Find the interval of convergence of each of the...Ch. 1.10 - Find the interval of convergence of each of the...Ch. 1.10 - Find the interval of convergence of each of the...Ch. 1.10 - Find the interval of convergence of each of the...Ch. 1.10 - Find the interval of convergence of each of the...Ch. 1.10 - The following series are not power series, but you...Ch. 1.10 - The following series are not power series, but you...Ch. 1.10 - The following series are not power series, but you...Ch. 1.10 - The following series are not power series, but you...Ch. 1.10 - The following series are not power series, but you...Ch. 1.10 - The following series are not power series, but you...Ch. 1.10 - The following series are not power series, but you...Ch. 1.12 - By the method used to obtain (12.5) [which is the...Ch. 1.13 - Use the ratio test to show that a binomial series...Ch. 1.13 - Show that the binomial coefficients 1n=(1)n.Ch. 1.13 - Show that if p is a positive integer, then pn=0...Ch. 1.13 - Write the Maclaurin series for 1/1+x in form...Ch. 1.13 - Using the methods of this section: Find the first...Ch. 1.13 - Using the methods of this section: Find the first...Ch. 1.13 - Using the methods of this section: Find the first...Ch. 1.13 - Using the methods of this section: Find the first...Ch. 1.13 - Using the methods of this section: Find the first...Ch. 1.13 - Using the methods of this section: Find the first...Ch. 1.13 - Using the methods of this section: Find the first...Ch. 1.13 - Using the methods of this section: Find the first...Ch. 1.13 - Using the methods of this section: Find the first...Ch. 1.13 - Using the methods of this section: Find the first...Ch. 1.13 - Using the methods of this section: Find the first...Ch. 1.13 - Using the methods of this section: Find the first...Ch. 1.13 - Using the methods of this section: Find the first...Ch. 1.13 - Using the methods of this section: Find the first...Ch. 1.13 - Using the methods of this section: Find the first...Ch. 1.13 - Find the first few terms of the Maclaurin series...Ch. 1.13 - Find the first few terms of the Maclaurin series...Ch. 1.13 - Find the first few terms of the Maclaurin series...Ch. 1.13 - Find the first few terms of the Maclaurin series...Ch. 1.13 - Find the first few terms of the Maclaurin series...Ch. 1.13 - Find the first few terms of the Maclaurin series...Ch. 1.13 - Find the first few terms of the Maclaurin series...Ch. 1.13 - Find the first few terms of the Maclaurin series...Ch. 1.13 - Find the first few terms of the Maclaurin series...Ch. 1.13 - Find the first few terms of the Maclaurin series...Ch. 1.13 - Find the first few terms of the Maclaurin series...Ch. 1.13 - Find the first few terms of the Maclaurin series...Ch. 1.13 - Find the first few terms of the Maclaurin series...Ch. 1.13 - Find the first few terms of the Maclaurin series...Ch. 1.13 - Find the first few terms of the Maclaurin series...Ch. 1.13 - Find the first few terms of the Maclaurin series...Ch. 1.13 - Find the first few terms of the Maclaurin series...Ch. 1.13 - In cos x Hints: Method l: Write cos x = 1+(cos...Ch. 1.13 - Find the first few terms of the Maclaurin series...Ch. 1.13 - Using method F above, find the first few terms of...Ch. 1.13 - Using method F above, find the first few terms of...Ch. 1.13 - Using method F above, find the first few terms of...Ch. 1.13 - Using method F above, find the first few terms of...Ch. 1.13 - Using method F above, find the first few terms of...Ch. 1.13 - Using method F above, find the first few terms of...Ch. 1.14 - Prove theorem (14.3). Hint: Group the terms in the...Ch. 1.14 - Using computer or tables (or Chapter 7, Section...Ch. 1.14 - In Problem 3 to 7, assume that the Maclaurin...Ch. 1.14 - In Problem 3 to 7, assume that the Maclaurin...Ch. 1.14 - In Problem 3 to 7, assume that the Maclaurin...Ch. 1.14 - In Problem 3 to 7, assume that the Maclaurin...Ch. 1.14 - In Problem 3 to 7, assume that the Maclaurin...Ch. 1.14 - Estimate the error if n=1xn/n3 is approximated by...Ch. 1.14 - Consider the series in Problem 4.6 and show that...Ch. 1.14 - Show that the interval of convergence of the...Ch. 1.14 - Show that the Maclaurin series for sin x converges...Ch. 1.14 - Show as in Problem 11 that the Maclaurin series...Ch. 1.14 - Show that Maclaurin for (1+x)p converges to (1+x)p...Ch. 1.15 - In problems 1 to 4, use power series to evaluate...Ch. 1.15 - In problems 1 to 4, use power series to evaluate...Ch. 1.15 - In problems 1 to 4, use power series to evaluate...Ch. 1.15 - In problems 1 to 4, use power series to evaluate...Ch. 1.15 - Use Maclaurin series to evaluate each of the...Ch. 1.15 - Use Maclaurin series to evaluate each of the...Ch. 1.15 - Use Maclaurin series to evaluate each of the...Ch. 1.15 - Use Maclaurin series to evaluate each of the...Ch. 1.15 - Use Maclaurin series to evaluate each of the...Ch. 1.15 - Use Maclaurin series to evaluate each of the...Ch. 1.15 - Use Maclaurin series to evaluate each of the...Ch. 1.15 - Use Maclaurin series to evaluate each of the...Ch. 1.15 - Use Maclaurin series to evaluate each of the...Ch. 1.15 - Find a two term aproximation for each of the...Ch. 1.15 - Find a two term aproximation for each of the...Ch. 1.15 - Find the sum of each of the following series by...Ch. 1.15 - Find the sum of each of the following series by...Ch. 1.15 - Find the sum of each of the following series by...Ch. 1.15 - Find the sum of each of the following series by...Ch. 1.15 - By computer or tables, find the exact sum of each...Ch. 1.15 - By computer, find a numerical approximation for...Ch. 1.15 - The series n=11/n8,s1, is called the Riemann Zeta...Ch. 1.15 - Find the following limits using Maclaurin series...Ch. 1.15 - Evaluate the following indeterminate forms by...Ch. 1.15 - In general, we do not expect Maclaurin series to...Ch. 1.15 - Find the values of several derivatives of...Ch. 1.15 - The velocity of electrons from a high energy...Ch. 1.15 - The energy of an electron at speed in special...Ch. 1.15 - The figure shows a heavy weight suspended by a...Ch. 1.15 - Prob. 30PCh. 1.15 - A tall tower of circular cross section is...Ch. 1.15 - Show that the doubling time (time for your money...Ch. 1.15 - If you are at the top Of a tower Of height h above...Ch. 1.16 - Show that it is possible to stack a pile of...Ch. 1.16 - The picture is a mobile constructed of dowels (or...Ch. 1.16 - Show that n=21/n3/2 is convergent. What is wrong...Ch. 1.16 - Test for convergence: n=12nn!Ch. 1.16 - Test for convergence: n=2(n1)21+n2Ch. 1.16 - Test for convergence: n=2n1(n+1)21Ch. 1.16 - Test for convergence: n=21n1n(n)3Ch. 1.16 - Test for convergence: n=22n3n42Ch. 1.16 - Find the interval of convergence, including...Ch. 1.16 - Find the interval of convergence, including...Ch. 1.16 - Find the interval of convergence, including...Ch. 1.16 - Find the interval of convergence, including...Ch. 1.16 - Find the interval of convergence, including...Ch. 1.16 - Find the Maclaurin series for the folliwing...Ch. 1.16 - Find the Maclaurin series for the folliwing...Ch. 1.16 - Find the Maclaurin series for the folliwing...Ch. 1.16 - Find the Maclaurin series for the folliwing...Ch. 1.16 - Find the Maclaurin series for the folliwing...Ch. 1.16 - Find the few terms of the Taylor series for the...Ch. 1.16 - Find the few terms of the Taylor series for the...Ch. 1.16 - Find the few terms of the Taylor series for the...Ch. 1.16 - Use the series you know to show that:...Ch. 1.16 - Use the series you know to show that:...Ch. 1.16 - Use the series you know to show that:...Ch. 1.16 - Evaluate the limit limx0x2/1ncosx by series (in...Ch. 1.16 - Use Maclaurin to do Problem 26 to 29 and check...Ch. 1.16 - Use Maclaurin to do Problem 26 to 29 and check...Ch. 1.16 - Use Maclaurin to do Problem 26 to 29 and check...Ch. 1.16 - Use Maclaurin to do Problem 26 to 29 and check...Ch. 1.16 - It is clear that you (or your computer) cant find...Ch. 1.16 - As in Problem 30, for each of the following...

Additional Math Textbook Solutions

Find more solutions based on key concepts
A pool is surrounded by a brick walkway as shown in the diagram. The pool is 3 feet deep and the walkway is 4 f...

Mathematics All Around (6th Edition)

The table by using the given graph of h.

Calculus for Business, Economics, Life Sciences, and Social Sciences (13th Edition)

In Problems 1 -6, express the given system of differential equations in matrix notation. x=7x+2y,y=3x2y

Fundamentals of Differential Equations and Boundary Value Problems

Checkpoint1 Use the substitution method to solve this system: Answers to Checkpoint exercises are found at the...

Mathematics with Applications In the Management, Natural, and Social Sciences (12th Edition)

Lemonade. You want to buy a new car, and you know the model you want. The model has three options, each one of ...

The Heart of Mathematics: An Invitation to Effective Thinking

Paul used 34 cup of butter in the batch of brownies he made. He ate 16 of the batch of brownies. What fraction ...

Mathematics for Elementary Teachers with Activities (5th Edition)

Knowledge Booster
Background pattern image
Math
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.
Similar questions
SEE MORE QUESTIONS
Recommended textbooks for you
Text book image
Elementary Linear Algebra (MindTap Course List)
Algebra
ISBN:9781305658004
Author:Ron Larson
Publisher:Cengage Learning
SEE MORE TEXTBOOKS
Sequences and Series Introduction; Author: Mario's Math Tutoring;https://www.youtube.com/watch?v=m5Yn4BdpOV0;License: Standard YouTube License, CC-BY
Introduction to sequences; Author: Dr. Trefor Bazett;https://www.youtube.com/watch?v=VG9ft4_dK24;License: Standard YouTube License, CC-BY