/*! 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. 15 If limk→∞akbk=∞ and ∑... [FREE SOLUTION] | 91Ó°ÊÓ

91Ó°ÊÓ

Log out

Learning Materials

Features

Discover

Chapter 7: Q. 15 (page 631)

Iflimk→∞akbk=∞and∑k=1∞_____Convergesthen∑k=1∞_____(converges/diverges).

Short Answer

Expert verified

Thefirstblankisfilledwith∑k=1∞bkandsecondwith∑k=1∞ak.

Step by step solution

01

Step 1. Given information

limk→∞akbk=∞

02

Step 2.. Limit comparison test  

ThelimitcomparisonteststatesthatforandbetwoserieswithpositivetermsthenIflimk→∞akbk=LWhereLisanypositiverealnumbertheneitherbothconvergesordiverges.Iflimk→∞akbk=0and∑k=1∞bkconvergesthen∑k=1∞akconverges.Iflimk→∞akbk=∞and∑k=1∞bkdivergesthen∑k=1∞akdiverges.

03

Step 3. Result

Iflimk→∞akbk=∞and∑k=1∞bkConvergesthen∑k=1∞akConvergesTherefore,thefirstblankisfilledwith∑k=1∞bkandsecondwith∑k=1∞ak.

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 91Ó°ÊÓ!

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

Leila finds that there are more factors affecting the number of salmon that return to Redfish Lake than the dams: There are good years and bad years. These happen at random, but they are more or less cyclical, so she models the number of fish qkreturning each year as qk+1=(0.14(−1)k+0.36)(qk+h), where h is the number of fish whose spawn she releases from the hatchery annually.

(a) Show that the sustained number of fish returning in even-numbered years approach approximately qe=3h∑k=1∞0.11k.

(Hint: Make a new recurrence by using two steps of the one given.)

(b) Show that the sustained number of fish returning in odd-numbered years approaches approximately qo=6111h∑k=1∞0.11k.

(c) How should Leila choose h, the number of hatchery fish to breed in order to hold the minimum number of fish returning in each run near some constant P?

Use either the divergence test or the integral test to determine whether the series in Exercises 32–43 converge or diverge. Explain why the series meets the hypotheses of the test you select.

35.∑k=1∞k2+k2

Determine whether the series ∑k=0∞-3k+14k-2converges or diverges. Give the sum of the convergent series.

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.

∑k=4∞ 2k−4k2−4k+3

In Exercises 48–51 find all values of p so that the series converges.

∑k=2∞1klnkp
See all solutions

Recommended explanations on Math Textbooks

Geometry

Read Explanation

Decision Maths

Read Explanation

Mechanics Maths

Read Explanation

Logic and Functions

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.