/*! 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. 25 For each of the sequences in Exe... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 7: Q. 25 (page 604)

For each of the sequences in Exercises 23鈥�52 determine whether the sequence is monotonic or eventually monotonic and whether the sequence is bounded above and/or below. If the sequence converges, give the limit.

25.sink蟺2

Short Answer

Expert verified

The sequence is not monotonic and bounded and not convergent.

The sequence has no limit.

Step by step solution

01

Step 1. Given information

We have been given the sequencesink蟺2.

02

Step 2. Determine whether the sequence is monotonic or eventually monotonic and whether the sequence is bounded above and/or below.

The sequence ak=sink蟺2is not a monotonic sequence because sign of sink蟺2varies as kincreases.

The sequence ak=sink蟺2is a bounded sequence because

-1鈮�sink蟺2鈮�1

The given sequence has upper and lower bound, therefore, the sequence is bounded.

The sequence is not monotonic but is bounded. Therefore, the sequence is not convergent and has no limit.

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

Determine whether the series 803-203+53-512+鈥�converges 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.

鈭�k=2鈭�鈥�1k(ln鈦�k)2

Determine whether the series 鈭�k=0鈭�-98kconverges 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)?

Find the values of x for which the series 鈭�K=0鈭�sinxkconverges.
See all solutions

Recommended explanations on Math Textbooks

Pure Maths

Read Explanation

Logic and Functions

Read Explanation

Applied Mathematics

Read Explanation

Calculus

Read Explanation

Probability and Statistics

Read Explanation

Geometry

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.