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# Solutions for Chapter 9.2: Tests for Absolute Convergence

## Full solutions for Introduction to Real Analysis | 3rd Edition

ISBN: 9780471321484

Solutions for Chapter 9.2: Tests for Absolute Convergence

Solutions for Chapter 9.2
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##### ISBN: 9780471321484

Since 20 problems in chapter 9.2: Tests for Absolute Convergence have been answered, more than 8713 students have viewed full step-by-step solutions from this chapter. Introduction to Real Analysis was written by and is associated to the ISBN: 9780471321484. This textbook survival guide was created for the textbook: Introduction to Real Analysis, edition: 3. Chapter 9.2: Tests for Absolute Convergence includes 20 full step-by-step solutions. This expansive textbook survival guide covers the following chapters and their solutions.

Key Calculus Terms and definitions covered in this textbook
• Additive identity for the complex numbers

0 + 0i is the complex number zero

• Additive inverse of a complex number

The opposite of a + bi, or -a - bi

• Angle of elevation

The acute angle formed by the line of sight (upward) and the horizontal

• equation of a parabola

(x - h)2 = 4p(y - k) or (y - k)2 = 4p(x - h)

• First quartile

See Quartile.

• Horizontal translation

A shift of a graph to the left or right.

• Identity

An equation that is always true throughout its domain.

• Inferential statistics

Using the science of statistics to make inferences about the parameters in a population from a sample.

• Initial value of a function

ƒ 0.

• Parameter interval

See Parametric equations.

• Position vector of the point (a, b)

The vector <a,b>.

• Quotient rule of logarithms

logb a R S b = logb R - logb S, R > 0, S > 0

• Sinusoid

A function that can be written in the form f(x) = a sin (b (x - h)) + k or f(x) = a cos (b(x - h)) + k. The number a is the amplitude, and the number h is the phase shift.

• Solve an equation or inequality

To find all solutions of the equation or inequality

• Standard representation of a vector

A representative arrow with its initial point at the origin

• Sum of an infinite series

See Convergence of a series

• Sum of complex numbers

(a + bi) + (c + di) = (a + c) + (b + d)i

• Vector

An ordered pair <a, b> of real numbers in the plane, or an ordered triple <a, b, c> of real numbers in space. A vector has both magnitude and direction.

• Weighted mean

A mean calculated in such a way that some elements of the data set have higher weights (that is, are counted more strongly in determining the mean) than others.

• z-coordinate

The directed distance from the xy-plane to a point in space, or the third number in an ordered triple.

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