 3.6.1: Show that if (x,.) is an unbounded sequence, then there exists a pr...
 3.6.2: Give examples of properly divergent sequences (x,.) and (y,.) withY...
 3.6.3: Show that if x,. > 0 for all n eN, then lim(x,.) = 0 if and only if...
 3.6.4: Establish the proper divergence of the following sequences. (a) ( J...
 3.6.5: Is the sequence (n sin n) properly divergent?
 3.6.6: Let (x,.) be properly divergent and let (y,.) be such that lim(x,.y...
 3.6.7: Let (x,.) and (y,.) be sequences of positive numbers such that lim(...
 3.6.8: Investigate the convergence or the divergence of the following sequ...
 3.6.9: Let (x,.) and (y,.) be sequences of positive numbers such that lim(...
 3.6.10: Show that if lim(a,./n) = L, where L > 0, then lim(a,.) = +oo.
Solutions for Chapter 3.6: Properly Divergent Sequences
Full solutions for Introduction to Real Analysis  3rd Edition
ISBN: 9780471321484
Solutions for Chapter 3.6: Properly Divergent Sequences
Get Full SolutionsChapter 3.6: Properly Divergent Sequences includes 10 full stepbystep solutions. Introduction to Real Analysis was written by and is associated to the ISBN: 9780471321484. Since 10 problems in chapter 3.6: Properly Divergent Sequences have been answered, more than 6373 students have viewed full stepbystep solutions from this chapter. This textbook survival guide was created for the textbook: Introduction to Real Analysis, edition: 3. This expansive textbook survival guide covers the following chapters and their solutions.

Angular speed
Speed of rotation, typically measured in radians or revolutions per unit time

Arithmetic sequence
A sequence {an} in which an = an1 + d for every integer n ? 2 . The number d is the common difference.

Backtoback stemplot
A stemplot with leaves on either side used to compare two distributions.

Closed interval
An interval that includes its endpoints

Combination
An arrangement of elements of a set, in which order is not important

Division
a b = aa 1 b b, b Z 0

Elements of a matrix
See Matrix element.

Graph of an equation in x and y
The set of all points in the coordinate plane corresponding to the pairs x, y that are solutions of the equation.

Inequality
A statement that compares two quantities using an inequality symbol

Inverse cosecant function
The function y = csc1 x

Inverse properties
a + 1a2 = 0, a # 1a

Line of symmetry
A line over which a graph is the mirror image of itself

Lower bound test for real zeros
A test for finding a lower bound for the real zeros of a polynomial

Onetoone rule of exponents
x = y if and only if bx = by.

Orthogonal vectors
Two vectors u and v with u x v = 0.

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

Rectangular coordinate system
See Cartesian coordinate system.

Repeated zeros
Zeros of multiplicity ? 2 (see Multiplicity).

Root of a number
See Principal nth root.

Sum of a finite geometric series
Sn = a111  r n 2 1  r