Chapter 7: Q. 23 (page 604)

For each of the sequences in Exercises 23–52 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.
23. $\{11\}$

Short Answer

Expert verified

The sequence is monotonic and bounded and the convergent.

The limit of the sequence $\{a_{k}\} = \{11\}$ is $11$ .

Step by step solution

Step 1. Given information

We have been given the sequence $\{11\}$ .

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

The constant sequence is always monotonic and bounded.

The monotonic and bounded sequence is always convergent.

The sequence $\{a_{k}\} = \{11\}$ is convergent.

Step 3. Determine the limit of the sequence.

$\lim_{k \to \infty} a_{k} = \lim_{k \to \infty} (11) = 11$

Thus, the limit of the sequence $\{a_{k}\} = \{11\}$ is $11$ .

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.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

For each of the sequences in Exercises 23–52 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.
23. $\{11\}$

Short Answer

Step by step solution

Step 1. Given information

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

Step 3. Determine the limit of the sequence.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Statistics

Geometry

Calculus

Applied Mathematics

Decision Maths

Study anywhere. Anytime. Across all devices.

For each of the sequences in Exercises 23–52 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.23.11

Short Answer

Step by step solution

Step 1. Given information

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

Step 3. Determine the limit of the sequence.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Statistics

Geometry

Calculus

Applied Mathematics

Decision Maths

Study anywhere. Anytime. Across all devices.

For each of the sequences in Exercises 23–52 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.
23. $\{11\}$