 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 9715 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 vector
See Magnitude of a vector.

Algebraic expression
A combination of variables and constants involving addition, subtraction, multiplication, division, powers, and roots

Bounded above
A function is bounded above if there is a number B such that ƒ(x) ? B for all x in the domain of ƒ.

Complex number
An expression a + bi, where a (the real part) and b (the imaginary part) are real numbers

Expanded form of a series
A series written explicitly as a sum of terms (not in summation notation).

Exponential function
A function of the form ƒ(x) = a ? bx,where ?0, b > 0 b ?1

Firstdegree equation in x , y, and z
An equation that can be written in the form.

Limit at infinity
limx: qƒ1x2 = L means that ƒ1x2 gets arbitrarily close to L as x gets arbitrarily large; lim x: q ƒ1x2 means that gets arbitrarily close to L as gets arbitrarily large

Lower bound for real zeros
A number c is a lower bound for the set of real zeros of ƒ if ƒ(x) Z 0 whenever x < c

Multiplication property of equality
If u = v and w = z, then uw = vz

Polynomial function
A function in which ƒ(x)is a polynomial in x, p. 158.

Quotient of functions
a ƒ g b(x) = ƒ(x) g(x) , g(x) ? 0

Real part of a complex number
See Complex number.

Scalar
A real number.

Scientific notation
A positive number written as c x 10m, where 1 ? c < 10 and m is an integer.

Sum of functions
(ƒ + g)(x) = ƒ(x) + g(x)

Terminal side of an angle
See Angle.

Variable
A letter that represents an unspecified number.

Variation
See Power function.

Vertical translation
A shift of a graph up or down.