 8.4.1: (a) What is an alternating series? (b) Under what conditions does a...
 8.4.2: What can you say about the series in each of the following cases?(a...
 8.4.3: Test the series for convergence or divergence.4 7 4 8 4 9 4 10 4 11
 8.4.4: Test the series for convergence or divergence.3 4 5 5 7 6 9 7 11 8
 8.4.5: Test the series for convergence or divergence.
 8.4.6: Test the series for convergence or divergence.
 8.4.7: Test the series for convergence or divergence.
 8.4.8: Test the series for convergence or divergence.
 8.4.9: Test the series for convergence or divergence.
 8.4.10: Test the series for convergence or divergence.
 8.4.11: Is the 50th partial sum of the alternating series an overestimate o...
 8.4.12: Calculate the rst 10 partial sums of the series n1 1n1 n3and graph ...
 8.4.13: For what values of is the following series convergent? n1 1n1 np
 8.4.14: Show that the series is convergent. How many terms of the series do...
 8.4.15: Show that the series is convergent. How many terms of the series do...
 8.4.16: Show that the series is convergent. How many terms of the series do...
 8.4.17: Graph both the sequence of terms and the sequence of partial sums o...
 8.4.18: Graph both the sequence of terms and the sequence of partial sums o...
 8.4.19: Approximate the sum of the series correct to four decimal places.
 8.4.20: Approximate the sum of the series correct to four decimal places.
 8.4.21: Determine whether the series is absolutely convergent.
 8.4.22: Determine whether the series is absolutely convergent.
 8.4.23: Determine whether the series is absolutely convergent.
 8.4.24: Determine whether the series is absolutely convergent.
 8.4.25: Determine whether the series is absolutely convergent.
 8.4.26: Determine whether the series is absolutely convergent.
 8.4.27: Determine whether the series is absolutely convergent.
 8.4.28: Determine whether the series is absolutely convergent.
 8.4.29: Determine whether the series is absolutely convergent.
 8.4.30: Determine whether the series is absolutely convergent.
 8.4.31: Determine whether the series is absolutely convergent.
 8.4.32: Determine whether the series is absolutely convergent.
 8.4.33: Determine whether the series is absolutely convergent.
 8.4.34: Determine whether the series is absolutely convergent.
 8.4.35: The terms of a series are dened recursively by the equationsDetermi...
 8.4.36: A series is dened by the equationsDetermine whether converges or di...
 8.4.37: For which of the following series is the Ratio Test inconclusive (t...
 8.4.38: LetThe Root Test says the following: (i) If , then is absolutely co...
 8.4.39: LetThe Root Test says the following: (i) If , then is absolutely co...
 8.4.40: For which positive integers is the following series convergent? n!2...
 8.4.41: (a) Show that converges for all . (b) Deduce that for all .
 8.4.42: Around 1910, the Indian mathematician Srinivasa Ramanujan discovere...
Solutions for Chapter 8.4: OTHER CONVERGENCE TESTS
Full solutions for Single Variable Calculus: Concepts and Contexts (Stewart's Calculus Series)  4th Edition
ISBN: 9780495559726
Solutions for Chapter 8.4: OTHER CONVERGENCE TESTS
Get Full SolutionsChapter 8.4: OTHER CONVERGENCE TESTS includes 42 full stepbystep solutions. This textbook survival guide was created for the textbook: Single Variable Calculus: Concepts and Contexts (Stewart's Calculus Series), edition: 4. This expansive textbook survival guide covers the following chapters and their solutions. Since 42 problems in chapter 8.4: OTHER CONVERGENCE TESTS have been answered, more than 22318 students have viewed full stepbystep solutions from this chapter. Single Variable Calculus: Concepts and Contexts (Stewart's Calculus Series) was written by and is associated to the ISBN: 9780495559726.

Absolute value of a complex number
The absolute value of the complex number z = a + b is given by ?a2+b2; also, the length of the segment from the origin to z in the complex plane.

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

Cubic
A degree 3 polynomial function

Discriminant
For the equation ax 2 + bx + c, the expression b2  4ac; for the equation Ax2 + Bxy + Cy2 + Dx + Ey + F = 0, the expression B2  4AC

Domain of a function
The set of all input values for a function

Empty set
A set with no elements

equation of a parabola
(x  h)2 = 4p(y  k) or (y  k)2 = 4p(x  h)

Equivalent vectors
Vectors with the same magnitude and direction.

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

Higherdegree polynomial function
A polynomial function whose degree is ? 3

Interval notation
Notation used to specify intervals, pp. 4, 5.

Lefthand limit of f at x a
The limit of ƒ as x approaches a from the left.

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

nth root of unity
A complex number v such that vn = 1

Quotient rule of logarithms
logb a R S b = logb R  logb S, R > 0, S > 0

Root of a number
See Principal nth root.

Standard form of a complex number
a + bi, where a and b are real numbers

Stretch of factor c
A transformation of a graph obtained by multiplying all the xcoordinates (horizontal stretch) by the constant 1/c, or all of the ycoordinates (vertical stretch) of the points by a constant c, c, > 1.

Terminal point
See Arrow.

Vertical component
See Component form of a vector.