Module 21 - Answers |
Lesson 1 |
Answer 1 |
21.1.1
The first ten terms of the sequence are
As n gets larger subsequent terms in the sequence get closer to zero. |
Answer 2 |
21.1.2
The limit of the sequence as n approaches is 0. |
Answer 3 |
21.1.3 The points in the graph level off and approach a horizontal line. In other words, the graph has a horizontal asymptote. |
Answer 4 |
21.1.4
Plotting the terms of the sequence gives graphical evidence that the sequence converges. The window shown is [xmin, xmax] x [ymin, ymax] = [0, 20] x [2, 3] with nmin = 1 and nmax = 20.
A table of values of the terms of the sequence gives numerical evidence that the sequence converges.
The value of gives analytical proof that the sequence converges.
The sequence converges to e 2.71828. |
Lesson 2 |
Answer 1 |
21.2.1 |
Answer 2 |
21.2.2 The fact that the graph appears to level off and have a horizontal asymptote suggests that the sequence of partial sums may converge, which would mean that the infinite series converges. |
Answer 3 |
21.2.3
Because the limit of the ratio of the sequence of partial sums is less than 1, the series converges. |
Answer 4 |
21.2.4 In the previous table the 26th and 51st partial sums were both approximately 10.5. So a reasonable estimate for the sum of the infinite series is 10.5. |
Lesson 3 |
Answer 1 |
21.3.1
The sequence is known as the Fibonacci sequence: 1, 1, 2, 3, 5, 8, 13, 21, 34,... |
Self Test |
Answer 1 |
Answer 2 |
Answer 3 |
The sequence appears to converge to approximately 0.377. The actual value is |
Answer 4 |
Answer 5 |
Set
in the Y= Editor.
The series appears to converge to approximately 2.71828. The exact value is |
Answer 6 |
The sequence appears to converge to approximately 63.797. The exact value is 64. |
©Copyright 2007 All rights reserved. | Trademarks | Privacy Policy | Link Policy |