/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Q. 8 Explain how you could adapt the ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 7: Q. 8 (page 624)

Explain how you could adapt the integral test to analyze a series 鈭�k=1鈭�f(k)in which the functionf:[1,鈭�)鈫�鈩� is continuous, negative, and increasing.

Short Answer

Expert verified

By the integral test, the series 鈭�k=1鈭�f(k) is divergent.

Step by step solution

01

Step 1. Given Information.

The series:

鈭�k=1鈭�f(k)

02

Step 2. Integral test.

By the integral test, the function will both converge or diverge.

鈭�1鈭�-f(x)dx=limk鈫�鈭�鈭�1k-伪.dx=limk鈫�鈭�[-伪x]1k=limk鈫�鈭�[-伪k+伪]=0

03

Step 3. Convergent or divergent.

By the integral test, the improper integral 鈭�1鈭�f(x)dxis divergent.

So the series 鈭�k=1鈭�f(k)is divergent.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Consider the series

Fill in the blanks and select the correct word:

Iflimk鈫�鈭�akbk=鈭�and鈭�k=1鈭�_____divergesthen鈭�k=1鈭�_____(converges/diverges).

Use the divergence test to analyze the given series. Each answer should either be the series diverges or the divergence test fails, along with the reason for your answer.

鈭�k=1鈭�k3k+100

Explain why the integral test may be used to analyze the given series and then use the test to determine whether the series converges or diverges.

鈭�k=1鈭�鈥�(3k鈭�1)鈭�2/3

If limk鈫�鈭�akbkWhereLis a positive finite number, what may we conclude about the two series?
See all solutions

Recommended explanations on Math Textbooks

Applied Mathematics

Read Explanation

Statistics

Read Explanation

Probability and Statistics

Read Explanation

Decision Maths

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Discrete Mathematics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.