/*! 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. 62 In Exercises 59鈥�62 use the der... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 7: Q. 62 (page 592)

In Exercises 59鈥�62 use the derivative test in Theorem 7.6 to analyze the monotonicity of the given sequence.

k!k+1!

Short Answer

Expert verified

The given sequence is strictly decreasing.

Step by step solution

01

Step 1. Given Information.

The given sequence isk!k+1!.

02

Step 2. Use the derivative test. 

To analyze the monotonicity of the given sequence we will use the derivative test.

Let the function isf(k)=k!k+1!.

According to the derivative test,

role="math" localid="1649235471579" f(k)=k!(k+1)k!f(k)=1k+1f'(k)=k+10-11k+12f'(k)=-1k+12

Now,f'k<0forallk>0.

Therefore, the given sequence is strictly decreasing.

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

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

Determine whether the series 鈭�k=0鈭�32kconverges or diverges. Give the sum of the convergent series.

Let f(x) be a function that is continuous, positive, and decreasing on the interval [1,鈭�)such that role="math" localid="1649081384626" limx鈫�鈭�f(x)=伪>0. What can the divergence test tell us about the series 鈭�k=1鈭�f(k)?

Use any convergence test from this section or the previous section to determine whether the series in Exercises 31鈥�48 converge or diverge. Explain how the series meets the hypotheses of the test you select.

鈭�k=1鈭�12k+7

Improper Integrals: Determine whether the following improper integrals converge or diverge.

鈭�1鈭�1xdx.
See all solutions

Recommended explanations on Math Textbooks

Probability and Statistics

Read Explanation

Mechanics Maths

Read Explanation

Statistics

Read Explanation

Pure Maths

Read Explanation

Decision Maths

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.