 9.3.1: Test the following series for convergence and for absolute converge...
 9.3.2: If sn is the nth partial sum of the alternating series L~l (_1)n+l ...
 9.3.3: Give an example to show that the Alternating Series Test 9.3.2 may ...
 9.3.4: Show that the Alternating Series Test is a consequence of Dirichlet...
 9.3.5: Consider the series1 1 1 1 1 11 ++ ++...2 345 67'where the signs...
 9.3.6: Let an e JRfor n e N and let p < q. If the seriesL anInPis converge...
 9.3.7: If p and q are positive numbers, show that L ( _1)n (In n)P Inq is ...
 9.3.8: Discuss the series whose nth term is:nn nn(a) (_1)n. Hn+l' (b) _ _'...
 9.3.9: If the partial sums of L an are bounded, show that the series L~l a...
 9.3.10: If the partial sums sn of L~l an are bounded, show that the series ...
 9.3.11: Can Dirichlet's Test be applied to establish the convergence of1 1 ...
 9.3.12: Show that the hypotheses that the sequence X := (xn) is decreasing ...
 9.3.13: If (an) is a bounded decreasing sequence and (bn) is a bounded incr...
 9.3.14: Show that if the partial sums sn of the series L~l ak satisfy ISnI ...
 9.3.15: Suppose that L an is a convergent series of real numbers. Either pr...
Solutions for Chapter 9.3: Tests for Nonabsolute Convergence
Full solutions for Introduction to Real Analysis  3rd Edition
ISBN: 9780471321484
Solutions for Chapter 9.3: Tests for Nonabsolute Convergence
Get Full SolutionsSince 15 problems in chapter 9.3: Tests for Nonabsolute Convergence have been answered, more than 3145 students have viewed full stepbystep solutions from this chapter. Introduction to Real Analysis was written by and is associated to the ISBN: 9780471321484. This expansive textbook survival guide covers the following chapters and their solutions. Chapter 9.3: Tests for Nonabsolute Convergence includes 15 full stepbystep solutions. This textbook survival guide was created for the textbook: Introduction to Real Analysis, edition: 3.

Absolute value of a real number
Denoted by a, represents the number a or the positive number a if a < 0.

Circle graph
A circular graphical display of categorical data

Difference of functions
(ƒ  g)(x) = ƒ(x)  g(x)

Equivalent systems of equations
Systems of equations that have the same solution.

Explicitly defined sequence
A sequence in which the kth term is given as a function of k.

Halfplane
The graph of the linear inequality y ? ax + b, y > ax + b y ? ax + b, or y < ax + b.

Horizontal component
See Component form of a vector.

Horizontal translation
A shift of a graph to the left or right.

Imaginary part of a complex number
See Complex number.

Inverse reflection principle
If the graph of a relation is reflected across the line y = x , the graph of the inverse relation results.

Measure of center
A measure of the typical, middle, or average value for a data set

Natural logarithmic regression
A procedure for fitting a logarithmic curve to a set of data.

Ordered set
A set is ordered if it is possible to compare any two elements and say that one element is “less than” or “greater than” the other.

Quadrantal angle
An angle in standard position whose terminal side lies on an axis.

Quadratic regression
A procedure for fitting a quadratic function to a set of data.

Riemann sum
A sum where the interval is divided into n subintervals of equal length and is in the ith subinterval.

Sample standard deviation
The standard deviation computed using only a sample of the entire population.

Slopeintercept form (of a line)
y = mx + b

Transverse axis
The line segment whose endpoints are the vertices of a hyperbola.

xaxis
Usually the horizontal coordinate line in a Cartesian coordinate system with positive direction to the right,.
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