 9.3.1: In Exercises 13, find the first five terms of the sequence of parti...
 9.3.2: In Exercises 13, find the first five terms of the sequence of parti...
 9.3.3: In Exercises 13, find the first five terms of the sequence of parti...
 9.3.4: In Exercises 47, use the integral test to decide whether the series...
 9.3.5: In Exercises 47, use the integral test to decide whether the series...
 9.3.6: In Exercises 47, use the integral test to decide whether the series...
 9.3.7: In Exercises 47, use the integral test to decide whether the series...
 9.3.8: Use comparison with  1 x3 dx to show that * n=2 1/n3 converges to ...
 9.3.9: Use comparison with  1 x3 dx to show that * n=2 1/n3 converges to ...
 9.3.10: In Exercises 1012, explain why the integral test cannot be used to ...
 9.3.11: In Exercises 1012, explain why the integral test cannot be used to ...
 9.3.12: In Exercises 1012, explain why the integral test cannot be used to ...
 9.3.13: In 1332, does the series converge or diverge?
 9.3.14: In 1332, does the series converge or diverge?
 9.3.15: In 1332, does the series converge or diverge?
 9.3.16: In 1332, does the series converge or diverge?
 9.3.17: In 1332, does the series converge or diverge?
 9.3.18: In 1332, does the series converge or diverge?
 9.3.19: In 1332, does the series converge or diverge?
 9.3.20: In 1332, does the series converge or diverge?
 9.3.21: In 1332, does the series converge or diverge?
 9.3.22: In 1332, does the series converge or diverge?
 9.3.23: In 1332, does the series converge or diverge?
 9.3.24: In 1332, does the series converge or diverge?
 9.3.25: In 1332, does the series converge or diverge?
 9.3.26: In 1332, does the series converge or diverge?
 9.3.27: In 1332, does the series converge or diverge?
 9.3.28: In 1332, does the series converge or diverge?
 9.3.29: In 1332, does the series converge or diverge?
 9.3.30: In 1332, does the series converge or diverge?
 9.3.31: In 1332, does the series converge or diverge?
 9.3.32: In 1332, does the series converge or diverge?
 9.3.33: Show that+ n=1 1 ln(2n) diverges.
 9.3.34: Show that+ n=1 1 (ln(2n))2 converges.
 9.3.35: (a) Find the partial sum, Sn, of+ n=1 ln n + 1 n . (b) Does the ser...
 9.3.36: (a) Show rln n = nln r for positive numbers n and r. (b) For what v...
 9.3.37: Consider the series+ k=1 1 k(k + 1) = 1 1 2 + 1 2 3 + . (a) Show th...
 9.3.38: Consider the series+ k=1 1 k(k + 1) = 1 1 2 + 1 2 3 + . (a) Show th...
 9.3.39: Show that if *an and *bn converge and if k is a constant, then *(an...
 9.3.40: Let N be a positive integer. Show that if an = bn for n N, then *an...
 9.3.41: Show that if *an converges, then lim n an = 0. [Hint: Consider limn...
 9.3.42: Show that if *an diverges and k = 0, then *kan diverges.
 9.3.43: The series *an converges. Explain, by looking at partial sums, why ...
 9.3.44: The series *an diverges. Give examples that show the series *(an+1 ...
 9.3.45: In this problem, you will justify the integral test. Suppose c 0 an...
 9.3.46: Consider the following grouping of terms in the harmonic series: 1 ...
 9.3.47: Show that+ n=2 1 n ln n diverges. (a) Using the integral test. (b) ...
 9.3.48: Consider the sequence given by an = 1 + 1 2 + 1 3 + 1 n ln(n + 1). ...
 9.3.49: On page 509, we gave Eulers result + n=1 1 n2 = 2 6 . (a) Find the ...
 9.3.50: This problem approximates e using e = + n=0 1 n! . (a) Find a lower...
 9.3.51: In this problem we investigate how fast the partial sums SN = 15 + ...
 9.3.52: In 1913, the English mathematician G. H. Hardy received a letter fr...
 9.3.53: In 5354, explain what is wrong with the statement.
 9.3.54: In 5354, explain what is wrong with the statement.
 9.3.55: A series * n=1 * an with limn an = 0, but such that n=1 an diverges.
 9.3.56: A convergent series * n=1 an, whose terms are all posi
 9.3.57: Decide if the statements in 5764 are true or false. Give an explana...
 9.3.58: Decide if the statements in 5764 are true or false. Give an explana...
 9.3.59: Decide if the statements in 5764 are true or false. Give an explana...
 9.3.60: Decide if the statements in 5764 are true or false. Give an explana...
 9.3.61: Decide if the statements in 5764 are true or false. Give an explana...
 9.3.62: Decide if the statements in 5764 are true or false. Give an explana...
 9.3.63: Decide if the statements in 5764 are true or false. Give an explana...
 9.3.64: Decide if the statements in 5764 are true or false. Give an explana...
 9.3.65: Which of the following defines a convergent sequence of partial sum...
Solutions for Chapter 9.3: CONVERGENCE OF SERIES
Full solutions for Calculus: Single Variable  6th Edition
ISBN: 9780470888643
Solutions for Chapter 9.3: CONVERGENCE OF SERIES
Get Full SolutionsSince 65 problems in chapter 9.3: CONVERGENCE OF SERIES have been answered, more than 35289 students have viewed full stepbystep solutions from this chapter. Chapter 9.3: CONVERGENCE OF SERIES includes 65 full stepbystep solutions. This expansive textbook survival guide covers the following chapters and their solutions. Calculus: Single Variable was written by and is associated to the ISBN: 9780470888643. This textbook survival guide was created for the textbook: Calculus: Single Variable , edition: 6.

Arcsine function
See Inverse sine function.

Bias
A flaw in the design of a sampling process that systematically causes the sample to differ from the population with respect to the statistic being measured. Undercoverage bias results when the sample systematically excludes one or more segments of the population. Voluntary response bias results when a sample consists only of those who volunteer their responses. Response bias results when the sampling design intentionally or unintentionally influences the responses

Boxplot (or boxandwhisker plot)
A graph that displays a fivenumber summary

Conversion factor
A ratio equal to 1, used for unit conversion

Dihedral angle
An angle formed by two intersecting planes,

Equivalent arrows
Arrows that have the same magnitude and direction.

Focal axis
The line through the focus and perpendicular to the directrix of a conic.

Frequency
Reciprocal of the period of a sinusoid.

Frequency (in statistics)
The number of individuals or observations with a certain characteristic.

Graph of a function ƒ
The set of all points in the coordinate plane corresponding to the pairs (x, ƒ(x)) for x in the domain of ƒ.

Hyperbola
A set of points in a plane, the absolute value of the difference of whose distances from two fixed points (the foci) is a constant.

Identity matrix
A square matrix with 1’s in the main diagonal and 0’s elsewhere, p. 534.

Mode of a data set
The category or number that occurs most frequently in the set.

Modulus
See Absolute value of a complex number.

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)

Power regression
A procedure for fitting a curve y = a . x b to a set of data.

Principle of mathematical induction
A principle related to mathematical induction.

Sample survey
A process for gathering data from a subset of a population, usually through direct questioning.

Semiperimeter of a triangle
Onehalf of the sum of the lengths of the sides of a triangle.

Vertical stretch or shrink
See Stretch, Shrink.