Chapter 1: Q9P (page 32)

$\frac{1 + x}{1 - x}$

Short Answer

Expert verified

The series is $\frac{1 + x}{1 - x} = 1 + \sum_{n = 1}^{\infty} 2 x^{n}$ .

The sum is given below.

$S_{1} = 1 + 2 x$

$S_{2} = 1 + 2 x + 2 x^{2}$

$S_{3} = 1 + 2 x + 2 x^{2} + 2 x^{3}$

The graphs are shown below.

Step by step solution

Step 1: Given Information

The Maclaurin series.

Definition of the MaclaurinSeries.

A Maclaurin series is a function with an expansion series that gives the sum of the function's derivatives.

Find the series and sum.

The Maclaurin series is given below.

$\frac{1 + x}{1 - x} = 1 + 2 x + 2 x^{2} + 2 x^{3} + \dots$

The general series is given below.

$\frac{1 + x}{1 - x} = 1 + \sum_{n = 1}^{\infty} 2 x^{n}$

The sum is given below.

$S_{1} = 1 + 2 x$

$S_{2} = 1 + 2 x + 2 x^{2}$

$S_{3} = 1 + 2 x + 2 x^{2} + 2 x^{3}$

Plot the graphs.

The graph of the function with $S_{1}, S_{2}, S_{3}$ is given below.

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 Physics Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

$\frac{1 + x}{1 - x}$

Short Answer

Step by step solution

Step 1: Given Information

Definition of the MaclaurinSeries.

Find the series and sum.

Plot the graphs.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Waves Physics

Classical Mechanics

Kinematics Physics

Circular Motion and Gravitation

Oscillations

Further Mechanics and Thermal Physics

Study anywhere. Anytime. Across all devices.

1+x1-x

Short Answer

Step by step solution

Step 1: Given Information

Definition of the MaclaurinSeries.

Find the series and sum.

Plot the graphs.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Waves Physics

Classical Mechanics

Kinematics Physics

Circular Motion and Gravitation

Oscillations

Further Mechanics and Thermal Physics

Study anywhere. Anytime. Across all devices.

$\frac{1 + x}{1 - x}$