   Chapter 11.1, Problem 22E

Chapter
Section
Textbook Problem

Calculate, to four decimal places, the first ten terms of the sequence and use them to plot the graph of the sequence by hand. Does the sequence appear to have a limit? If so, calculate it. If not, explain why.22. a n = 1 + 10 n 9 n

To determine

To find: The first ten terms of the sequence and plot them on the graph to obtain the limit.

Explanation

Given:

The sequence is an=1+109nn.                                                                                  …… (1)

Calculation:

Consider the sequence an=1+109nn.

Obtain the first ten terms of the sequence.

Substitute 1 for n in equation (1),

a1=1+10191   =1+109   =199   =2.1111

Thus, the first term of the sequence is a1=2.1111_.

Substitute 2 for n in equation (1),

a2=1+10292   =1+10081   =18181   =2.2346

Thus, the second term of the sequence is a2=2.2346_.

Substitute 3 for n in equation (1).

a3=1+10393   =1+1,000729   =1,729729   =2.3717

Thus, the third term of the sequence is a3=2.3717_.

Substitute 4 for n in equation (1).

a4=1+10494   =1+10,0006,561   =16,5616,561   =2.5242

Thus, the fourth term of the sequence is a4=2.5242_.

Substitute 5 for n in equation (1).

a5=1+10595   =1+100,00059,049   =159,04959,049   =2.6935

Thus, the fifth term of the sequence is a5=2.6935_.

Substitute 6 for n in equation (1).

a6=1+10696   =1+1,000,000531,441   =1,531,441531,441   =2.8817

Thus, the sixth term of the sequence is a6=2.8817_.

Substitute 7 for n in equation (1).

a7=1+10797   =1+10,000,0004,782,969   =14,782,9694,782,969   =3.0908

Thus, the seventh term of the sequence is a7=3.0908_.

Substitute 8 for n in equation (1).

a8=1+10898   =1+100,000,00043,046,721   =143,046,72143,046,721   =3.3231

Thus, the eighth term of the sequence is a8=3.3231_.

Substitute 9 for n in equation (1).

a9=1+10999   =1+1,000,000,000387,420,489   =1,387,420,489387,420,489   =3

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

Convert the expressions in Exercises 8596 radical form. 94(1x)7/3

Finite Mathematics and Applied Calculus (MindTap Course List)

In Exercises 2932, find the value(s) of x that satisfy the expression. 29. 2x2 + 3x 2 0

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

Name each polygon:

Elementary Technical Mathematics

The graph of x = cos t, y = sin2 t is:

Study Guide for Stewart's Multivariable Calculus, 8th 