   Chapter 11.1, Problem 58E

Chapter
Section
Textbook Problem

# Use a graph of the sequence to decide whether the sequence is convergent or divergent. If the sequence is convergent, guess the value of the limit from the graph and then prove your guess. (See the margin note on page 739 for advice on graphing sequences.)58. a n = sin n n

To determine

Whether the sequence is convergent or divergent; guess the value of the limit if convergent with valid proof.

Explanation

Given:

The sequence is an=sinnn .

Definition used:

If an is a sequence and limnan exists, then the sequence an is said to be convergent; otherwise it is divergent.

Theorem used: Squeeze Theorem

If xnznyn for nN and limnxn=limnyn=l , then limnzn=l . (1)

Calculation:

Obtain the first 20 terms of the sequence.

 n sinn an=sinnn 1 sin1=0.8415 0.84151=0.8415 2 sin2=0.9093 0.90932=0.4547 3 sin3=0.1411 0.14113=0.0470 4 sin4=−0.7568 −0.75684=−0.1892 5 sin5=−0.9589 −0.95895=−0.1918 6 sin6=−0.2794 −0.27946=−0.0466 7 sin7=0.6570 0.65707=0.0939 8 sin8=0.9894 0.98948=0.1237 9 sin9=0.4121 0.41219=0.0458 10 sin10=−0.5440 −0.544010=−0.0544 11 sin11=−1.0000 −1.000011=0.0909 12 sin12=−0.5366 −0.536612=−0.0447 13 sin13=0.4202 0.420213=0.0323 14 sin14=0

### Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

#### The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

#### Solve the equations in Exercises 126. (x+1)2(2x+3)(x+1)(2x+3)2=0

Finite Mathematics and Applied Calculus (MindTap Course List)

#### Find the domain of the function. a. f(x) = 9x b. f(x) = x+32x2x3

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

#### Change1.5g/cm2tomg/mm2.

Elementary Technical Mathematics

#### The normal plane to at t = 1 has equation:

Study Guide for Stewart's Multivariable Calculus, 8th 