 9.2.1: Establish the convergence or the divergence of the series whose nth...
 9.2.2: Establish the convergence or divergence of the series whose nth ten...
 9.2.3: Discuss the convergence or the divergence of the series with nth te...
 9.2.4: Discuss the convergence or the divergence of the series with nth te...
 9.2.5: Show that the series 1/12 + 1/23 + 1/32 + 1/43 +... is convergent, ...
 9.2.6: If a and b are positive numbers, then ~)an + b)P converges if p > ...
 9.2.7: Discuss the series whose nth tenn isn! (n!)2(b) (2n)!'2 .4 .. .(2n)...
 9.2.8: Let 0 < a < 1 and consider the seriesa2 + a + a4 + a3 +... + a2n+ a...
 9.2.9: Ifr E (0, 1) satisfies (2) in the Root Test 9.2.2, show that the pa...
 9.2.10: Ifr E (0, 1) satisfies (5) in the Ratio Test 9.2.4, show that Is  ...
 9.2.11: If a > 1 satisfies (to) in Raabe's Test 9.2.8, show that Is  sn I ...
 9.2.12: For each of the series in Exercise 1 that converge, estimate the re...
 9.2.13: Answer the questions posed in Exercise 12 for the series given in E...
 9.2.14: Show that the series 1 + !  ~ + 1 + k  ~ + +  ... is divergent
 9.2.15: For n EN, let cn be defined by cn := t + ! +... + l/n Inn. Show th...
 9.2.16: Let {nl, n2, ...} denote the collection of natural numbers that do ...
 9.2.17: If P > 0, q > 0, show that the seriesL ((pq ++ ll))((qp ++ 22)).......
 9.2.18: Suppose that none of the numbersa, b, e is a negativeintegeror zero...
 9.2.19: Let an > 0 and suppose that L an converges. Construct a convergent ...
 9.2.20: Let (an) be a decreasing sequence of real numbers converging to 0 a...
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
Get Full SolutionsSince 20 problems in chapter 9.2: Tests for Absolute Convergence have been answered, more than 8713 students have viewed full stepbystep 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 stepbystep solutions. This expansive textbook survival guide covers the following chapters and their solutions.

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.

zcoordinate
The directed distance from the xyplane to a point in space, or the third number in an ordered triple.