 9.6.1: In Exercises 14, verify the formula.
 9.6.2: In Exercises 14, verify the formula.
 9.6.3: In Exercises 14, verify the formula.
 9.6.4: In Exercises 14, verify the formula.
 9.6.5: In Exercises 510, match the series with the graph of its sequence o...
 9.6.6: In Exercises 510, match the series with the graph of its sequence o...
 9.6.7: In Exercises 510, match the series with the graph of its sequence o...
 9.6.8: In Exercises 510, match the series with the graph of its sequence o...
 9.6.9: In Exercises 510, match the series with the graph of its sequence o...
 9.6.10: In Exercises 510, match the series with the graph of its sequence o...
 9.6.11: Numerical, Graphical, and Analytic Analysis In Exercises 11 and 12,...
 9.6.12: Numerical, Graphical, and Analytic Analysis In Exercises 11 and 12,...
 9.6.13: In Exercises 1332, use the Ratio Test to determine the convergence ...
 9.6.14: In Exercises 1332, use the Ratio Test to determine the convergence ...
 9.6.15: In Exercises 1332, use the Ratio Test to determine the convergence ...
 9.6.16: In Exercises 1332, use the Ratio Test to determine the convergence ...
 9.6.17: In Exercises 1332, use the Ratio Test to determine the convergence ...
 9.6.18: In Exercises 1332, use the Ratio Test to determine the convergence ...
 9.6.19: In Exercises 1332, use the Ratio Test to determine the convergence ...
 9.6.20: In Exercises 1332, use the Ratio Test to determine the convergence ...
 9.6.21: In Exercises 1332, use the Ratio Test to determine the convergence ...
 9.6.22: In Exercises 1332, use the Ratio Test to determine the convergence ...
 9.6.23: In Exercises 1332, use the Ratio Test to determine the convergence ...
 9.6.24: In Exercises 1332, use the Ratio Test to determine the convergence ...
 9.6.25: In Exercises 1332, use the Ratio Test to determine the convergence ...
 9.6.26: In Exercises 1332, use the Ratio Test to determine the convergence ...
 9.6.27: In Exercises 1332, use the Ratio Test to determine the convergence ...
 9.6.28: In Exercises 1332, use the Ratio Test to determine the convergence ...
 9.6.29: In Exercises 1332, use the Ratio Test to determine the convergence ...
 9.6.30: In Exercises 1332, use the Ratio Test to determine the convergence ...
 9.6.31: In Exercises 1332, use the Ratio Test to determine the convergence ...
 9.6.32: In Exercises 1332, use the Ratio Test to determine the convergence ...
 9.6.33: In Exercises 3336, verify that the Ratio Test is inconclusive for t...
 9.6.34: In Exercises 3336, verify that the Ratio Test is inconclusive for t...
 9.6.35: In Exercises 3336, verify that the Ratio Test is inconclusive for t...
 9.6.36: In Exercises 3336, verify that the Ratio Test is inconclusive for t...
 9.6.37: In Exercises 37 50, use the Root Test to determine the convergence ...
 9.6.38: In Exercises 37 50, use the Root Test to determine the convergence ...
 9.6.39: In Exercises 37 50, use the Root Test to determine the convergence ...
 9.6.40: In Exercises 37 50, use the Root Test to determine the convergence ...
 9.6.41: In Exercises 37 50, use the Root Test to determine the convergence ...
 9.6.42: In Exercises 37 50, use the Root Test to determine the convergence ...
 9.6.43: In Exercises 37 50, use the Root Test to determine the convergence ...
 9.6.44: In Exercises 37 50, use the Root Test to determine the convergence ...
 9.6.45: In Exercises 37 50, use the Root Test to determine the convergence ...
 9.6.46: In Exercises 37 50, use the Root Test to determine the convergence ...
 9.6.47: In Exercises 37 50, use the Root Test to determine the convergence ...
 9.6.48: In Exercises 37 50, use the Root Test to determine the convergence ...
 9.6.49: In Exercises 37 50, use the Root Test to determine the convergence ...
 9.6.50: In Exercises 37 50, use the Root Test to determine the convergence ...
 9.6.51: In Exercises 5168, determine the convergence or divergence of the s...
 9.6.52: In Exercises 5168, determine the convergence or divergence of the s...
 9.6.53: In Exercises 5168, determine the convergence or divergence of the s...
 9.6.54: In Exercises 5168, determine the convergence or divergence of the s...
 9.6.55: In Exercises 5168, determine the convergence or divergence of the s...
 9.6.56: In Exercises 5168, determine the convergence or divergence of the s...
 9.6.57: In Exercises 5168, determine the convergence or divergence of the s...
 9.6.58: In Exercises 5168, determine the convergence or divergence of the s...
 9.6.59: In Exercises 5168, determine the convergence or divergence of the s...
 9.6.60: In Exercises 5168, determine the convergence or divergence of the s...
 9.6.61: In Exercises 5168, determine the convergence or divergence of the s...
 9.6.62: In Exercises 5168, determine the convergence or divergence of the s...
 9.6.63: In Exercises 5168, determine the convergence or divergence of the s...
 9.6.64: In Exercises 5168, determine the convergence or divergence of the s...
 9.6.65: In Exercises 5168, determine the convergence or divergence of the s...
 9.6.66: In Exercises 5168, determine the convergence or divergence of the s...
 9.6.67: In Exercises 5168, determine the convergence or divergence of the s...
 9.6.68: In Exercises 5168, determine the convergence or divergence of the s...
 9.6.69: In Exercises 6972, identify the two series that are the same.
 9.6.70: In Exercises 6972, identify the two series that are the same.
 9.6.71: In Exercises 6972, identify the two series that are the same.
 9.6.72: In Exercises 6972, identify the two series that are the same.
 9.6.73: In Exercises 73 and 74, write an equivalent series with the index o...
 9.6.74: In Exercises 73 and 74, write an equivalent series with the index o...
 9.6.75: In Exercises 75 and 76, (a) determine the number of terms required ...
 9.6.76: In Exercises 75 and 76, (a) determine the number of terms required ...
 9.6.77: In Exercises 7782, the terms of a series are defined recursively. D...
 9.6.78: In Exercises 7782, the terms of a series are defined recursively. D...
 9.6.79: In Exercises 7782, the terms of a series are defined recursively. D...
 9.6.80: In Exercises 7782, the terms of a series are defined recursively. D...
 9.6.81: In Exercises 7782, the terms of a series are defined recursively. D...
 9.6.82: In Exercises 7782, the terms of a series are defined recursively. D...
 9.6.83: In Exercises 8386, use the Ratio Test or the Root Test to determine...
 9.6.84: In Exercises 8386, use the Ratio Test or the Root Test to determine...
 9.6.85: In Exercises 8386, use the Ratio Test or the Root Test to determine...
 9.6.86: In Exercises 8386, use the Ratio Test or the Root Test to determine...
 9.6.87: In Exercises 8792, find the values of x for which the series conver...
 9.6.88: In Exercises 8792, find the values of x for which the series conver...
 9.6.89: In Exercises 8792, find the values of x for which the series conver...
 9.6.90: In Exercises 8792, find the values of x for which the series conver...
 9.6.91: In Exercises 8792, find the values of x for which the series conver...
 9.6.92: In Exercises 8792, find the values of x for which the series conver...
 9.6.93: State the Ratio Test.
 9.6.94: State the Root Test.
 9.6.95: You are told that the terms of a positive series appear toapproach ...
 9.6.96: The graph shows the first 10 terms of the sequence ofpartial sums o...
 9.6.97: Using the Ratio Test, it is determined that an alternating series c...
 9.6.98: Prove Property 2 of Theorem 9.17.
 9.6.99: Prove Theorem 9.18. (Hint for Property 1: If the limit equals choos...
 9.6.100: Show that the Root Test is inconclusive for the pseries
 9.6.101: Show that the Ratio Test and the Root Test are both inconclusive fo...
 9.6.102: Determine the convergence or divergence of the series when (a) (b) ...
 9.6.103: Show that if is absolutely convergent, then
 9.6.104: Writing Read the article A Differentiation Test for Absolute Conver...
 9.6.105: Is the following series convergent or divergent?
 9.6.106: Show that if the series converges, then the series converges also.
Solutions for Chapter 9.6: The Ratio and Root Tests
Full solutions for Calculus  8th Edition
ISBN: 9780618502981
Solutions for Chapter 9.6: The Ratio and Root Tests
Get Full SolutionsThis expansive textbook survival guide covers the following chapters and their solutions. Chapter 9.6: The Ratio and Root Tests includes 106 full stepbystep solutions. This textbook survival guide was created for the textbook: Calculus, edition: 8. Since 106 problems in chapter 9.6: The Ratio and Root Tests have been answered, more than 83105 students have viewed full stepbystep solutions from this chapter. Calculus was written by and is associated to the ISBN: 9780618502981.

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

Equal complex numbers
Complex numbers whose real parts are equal and whose imaginary parts are equal.

Equivalent vectors
Vectors with the same magnitude and direction.

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

Horizontal component
See Component form of a vector.

Hyperboloid of revolution
A surface generated by rotating a hyperbola about its transverse axis, p. 607.

Instantaneous rate of change
See Derivative at x = a.

Linear function
A function that can be written in the form ƒ(x) = mx + b, where and b are real numbers

Measure of center
A measure of the typical, middle, or average value for a data set

Monomial function
A polynomial with exactly one term.

Negative association
A relationship between two variables in which higher values of one variable are generally associated with lower values of the other variable.

Opens upward or downward
A parabola y = ax 2 + bx + c opens upward if a > 0 and opens downward if a < 0.

Permutation
An arrangement of elements of a set, in which order is important.

Sequence of partial sums
The sequence {Sn} , where Sn is the nth partial sum of the series, that is, the sum of the first n terms of the series.

Solution of a system in two variables
An ordered pair of real numbers that satisfies all of the equations or inequalities in the system

Sum identity
An identity involving a trigonometric function of u + v

Sum of two vectors
<u1, u2> + <v1, v2> = <u1 + v1, u2 + v2> <u1 + v1, u2 + v2, u3 + v3>

Transitive property
If a = b and b = c , then a = c. Similar properties hold for the inequality symbols <, >, ?, ?.

Unit vector
Vector of length 1.

Venn diagram
A visualization of the relationships among events within a sample space.