 9.4.1: Graphical Analysis The figures show the graphs of the first 10 term...
 9.4.2: Graphical Analysis The figures show the graphs of the first 10 term...
 9.4.3: Using the Direct Comparison Test In Exercises 312, use the Direct C...
 9.4.4: Using the Direct Comparison Test In Exercises 312, use the Direct C...
 9.4.5: Using the Direct Comparison Test In Exercises 312, use the Direct C...
 9.4.6: Using the Direct Comparison Test In Exercises 312, use the Direct C...
 9.4.7: Using the Direct Comparison Test In Exercises 312, use the Direct C...
 9.4.8: Using the Direct Comparison Test In Exercises 312, use the Direct C...
 9.4.9: Using the Direct Comparison Test In Exercises 312, use the Direct C...
 9.4.10: Using the Direct Comparison Test In Exercises 312, use the Direct C...
 9.4.11: Using the Direct Comparison Test In Exercises 312, use the Direct C...
 9.4.12: Using the Direct Comparison Test In Exercises 312, use the Direct C...
 9.4.13: Using the Limit Comparison Test In Exercises 1322, use the Limit Co...
 9.4.14: Using the Limit Comparison Test In Exercises 1322, use the Limit Co...
 9.4.15: Using the Limit Comparison Test In Exercises 1322, use the Limit Co...
 9.4.16: Using the Limit Comparison Test In Exercises 1322, use the Limit Co...
 9.4.17: Using the Limit Comparison Test In Exercises 1322, use the Limit Co...
 9.4.18: Using the Limit Comparison Test In Exercises 1322, use the Limit Co...
 9.4.19: Using the Limit Comparison Test In Exercises 1322, use the Limit Co...
 9.4.20: Using the Limit Comparison Test In Exercises 1322, use the Limit Co...
 9.4.21: Using the Limit Comparison Test In Exercises 1322, use the Limit Co...
 9.4.22: Using the Limit Comparison Test In Exercises 1322, use the Limit Co...
 9.4.23: Determining Convergence or Divergence In Exercises 2330, test for c...
 9.4.24: Determining Convergence or Divergence In Exercises 2330, test for c...
 9.4.25: Determining Convergence or Divergence In Exercises 2330, test for c...
 9.4.26: Determining Convergence or Divergence In Exercises 2330, test for c...
 9.4.27: Determining Convergence or Divergence In Exercises 2330, test for c...
 9.4.28: Determining Convergence or Divergence In Exercises 2330, test for c...
 9.4.29: Determining Convergence or Divergence In Exercises 2330, test for c...
 9.4.30: Determining Convergence or Divergence In Exercises 2330, test for c...
 9.4.31: Using the Limit Comparison Test Use the Limit Comparison Test with ...
 9.4.32: Proof Prove that, if and are polynomials of degree and respectively...
 9.4.33: Determining Convergence or Divergence In Exercises 3336, use the po...
 9.4.34: Determining Convergence or Divergence In Exercises 3336, use the po...
 9.4.35: Determining Convergence or Divergence In Exercises 3336, use the po...
 9.4.36: Determining Convergence or Divergence In Exercises 3336, use the po...
 9.4.37: Verifying Divergence In Exercises 37 and 38, use the divergence tes...
 9.4.38: Verifying Divergence In Exercises 37 and 38, use the divergence tes...
 9.4.39: Determining Convergence or Divergence In Exercises 3942, determine ...
 9.4.40: Determining Convergence or Divergence In Exercises 3942, determine ...
 9.4.41: Determining Convergence or Divergence In Exercises 3942, determine ...
 9.4.42: Determining Convergence or Divergence In Exercises 3942, determine ...
 9.4.43: Using Series Review the results of Exercises 3942. Explain why care...
 9.4.44: Direct Comparison Test State the Direct Comparison Test and give an...
 9.4.45: Limit Comparison Test State the Limit Comparison Test and give an e...
 9.4.46: Comparing Series It appears that the terms of the series are less t...
 9.4.47: Using a Series Consider the series (a) Verify that the series conve...
 9.4.48: HOW DO YOU SEE IT? The figure shows the first 20 terms of the conve...
 9.4.49: True or False? In Exercises 4954, determine whether the statement i...
 9.4.50: True or False? In Exercises 4954, determine whether the statement i...
 9.4.51: True or False? In Exercises 4954, determine whether the statement i...
 9.4.52: True or False? In Exercises 4954, determine whether the statement i...
 9.4.53: True or False? In Exercises 4954, determine whether the statement i...
 9.4.54: True or False? In Exercises 4954, determine whether the statement i...
 9.4.55: Proof Prove that if the nonnegative series and converge, then so do...
 9.4.56: Proof Use the result of Exercise 55 to prove that if the nonnegativ...
 9.4.57: Finding Series Find two series that demonstrate the result of Exerc...
 9.4.58: Finding Series Find two series that demonstrate the result of Exerc...
 9.4.59: Proof Suppose that and are series with positive terms. Prove that i...
 9.4.60: Proof Suppose that and are series with positive terms. Prove that i...
 9.4.61: Verifying Convergence Use the result of Exercise 59 to show that ea...
 9.4.62: Verifying Divergence Use the result of Exercise 60 to show that eac...
 9.4.63: Proof Suppose that is a series with positive terms. Prove that if c...
 9.4.64: Proof Prove that the series converges.
 9.4.65: Comparing Series Show that converges by comparison with
 9.4.66: Is the infinite series convergent? Prove your statement.
 9.4.67: Prove that if is a convergent series of positive real numbers, then...
Solutions for Chapter 9.4: Comparisons of Series
Full solutions for Calculus: Early Transcendental Functions  6th Edition
ISBN: 9781285774770
Solutions for Chapter 9.4: Comparisons of Series
Get Full SolutionsSince 67 problems in chapter 9.4: Comparisons of Series have been answered, more than 43722 students have viewed full stepbystep solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions. Chapter 9.4: Comparisons of Series includes 67 full stepbystep solutions. This textbook survival guide was created for the textbook: Calculus: Early Transcendental Functions, edition: 6. Calculus: Early Transcendental Functions was written by and is associated to the ISBN: 9781285774770.

Addition property of equality
If u = v and w = z , then u + w = v + z

Arrow
The notation PQ denoting the directed line segment with initial point P and terminal point Q.

Blocking
A feature of some experimental designs that controls for potential differences between subject groups by applying treatments randomly within homogeneous blocks of subjects

Convergence of a sequence
A sequence {an} converges to a if limn: q an = a

Course
See Bearing.

Equilibrium point
A point where the supply curve and demand curve intersect. The corresponding price is the equilibrium price.

Infinite discontinuity at x = a
limx:a + x a ƒ(x) = q6 or limx:a  ƒ(x) = q.

Multiplicity
The multiplicity of a zero c of a polynomial ƒ(x) of degree n > 0 is the number of times the factor (x  c) (x  z 2) Á (x  z n)

Observational study
A process for gathering data from a subset of a population through current or past observations. This differs from an experiment in that no treatment is imposed.

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.

Parallel lines
Two lines that are both vertical or have equal slopes.

Range of a function
The set of all output values corresponding to elements in the domain.

Sinusoidal regression
A procedure for fitting a curve y = a sin (bx + c) + d to a set of data

Sphere
A set of points in Cartesian space equally distant from a fixed point called the center.

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

Sum of an infinite series
See Convergence of a series

symmetric about the xaxis
A graph in which (x, y) is on the graph whenever (x, y) is; or a graph in which (r, ?) or (r, ?, ?) is on the graph whenever (r, ?) is

Synthetic division
A procedure used to divide a polynomial by a linear factor, x  a

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.

Zero of a function
A value in the domain of a function that makes the function value zero.