 9.2.1: In Exercises 16, find the first five terms of the sequence of parti...
 9.2.2: In Exercises 16, find the first five terms of the sequence of parti...
 9.2.3: In Exercises 16, find the first five terms of the sequence of parti...
 9.2.4: In Exercises 16, find the first five terms of the sequence of parti...
 9.2.5: In Exercises 16, find the first five terms of the sequence of parti...
 9.2.6: In Exercises 16, find the first five terms of the sequence of parti...
 9.2.7: In Exercises 716, verify that the infinite series diverges.n0 3 3 2 n
 9.2.8: In Exercises 716, verify that the infinite series diverges.n0 4 3 n
 9.2.9: In Exercises 716, verify that the infinite series diverges.n0 10001...
 9.2.10: In Exercises 716, verify that the infinite series diverges.n0 21.03n
 9.2.11: In Exercises 716, verify that the infinite series diverges.n1 n n 1
 9.2.12: In Exercises 716, verify that the infinite series diverges.n1 n 2n 3 n
 9.2.13: In Exercises 716, verify that the infinite series diverges.2 1 n1 n...
 9.2.14: In Exercises 716, verify that the infinite series diverges.n1 n n 2 1
 9.2.15: In Exercises 716, verify that the infinite series diverges.n n1 2n ...
 9.2.16: In Exercises 716, verify that the infinite series diverges.n1 n! 2 n
 9.2.17: In Exercises 1722, match the series with the graph of its sequence ...
 9.2.18: In Exercises 1722, match the series with the graph of its sequence ...
 9.2.19: In Exercises 1722, match the series with the graph of its sequence ...
 9.2.20: In Exercises 1722, match the series with the graph of its sequence ...
 9.2.21: In Exercises 1722, match the series with the graph of its sequence ...
 9.2.22: In Exercises 1722, match the series with the graph of its sequence ...
 9.2.23: In Exercises 2328, verify that the infinite series converges.n1 1 n...
 9.2.24: In Exercises 2328, verify that the infinite series converges.n1 1 n...
 9.2.25: In Exercises 2328, verify that the infinite series converges.n0 2 3...
 9.2.26: In Exercises 2328, verify that the infinite series converges.n1 2 1...
 9.2.27: In Exercises 2328, verify that the infinite series converges.n0 0.9...
 9.2.28: In Exercises 2328, verify that the infinite series converges.n0 0.6...
 9.2.29: Numerical, Graphical, and Analytic Analysis In Exercises 2934, (a) ...
 9.2.30: Numerical, Graphical, and Analytic Analysis In Exercises 2934, (a) ...
 9.2.31: Numerical, Graphical, and Analytic Analysis In Exercises 2934, (a) ...
 9.2.32: Numerical, Graphical, and Analytic Analysis In Exercises 2934, (a) ...
 9.2.33: Numerical, Graphical, and Analytic Analysis In Exercises 2934, (a) ...
 9.2.34: Numerical, Graphical, and Analytic Analysis In Exercises 2934, (a) ...
 9.2.35: In Exercises 3550, find the sum of the convergent series.nn 2 n2 1 ...
 9.2.36: In Exercises 3550, find the sum of the convergent series.n1 4 nn 2 n
 9.2.37: In Exercises 3550, find the sum of the convergent series.2n 12n 3 n...
 9.2.38: In Exercises 3550, find the sum of the convergent series.n1 1 2n 12...
 9.2.39: In Exercises 3550, find the sum of the convergent series.n0 1 2 n
 9.2.40: In Exercises 3550, find the sum of the convergent series.n0 6 4 5 n
 9.2.41: In Exercises 3550, find the sum of the convergent series.n0 1 2 n
 9.2.42: In Exercises 3550, find the sum of the convergent series.n0 2 2 3 n
 9.2.43: In Exercises 3550, find the sum of the convergent series.1 0. 0.01 ...
 9.2.44: In Exercises 3550, find the sum of the convergent series.8 6 9
 9.2.45: In Exercises 3550, find the sum of the convergent series.3 1 1
 9.2.46: In Exercises 3550, find the sum of the convergent series.4 2 1 1
 9.2.47: In Exercises 3550, find the sum of the convergent series.n0 1 2n 1 ...
 9.2.48: In Exercises 3550, find the sum of the convergent series.n1 0.7 n 0...
 9.2.49: In Exercises 3550, find the sum of the convergent series.n1 sin 1n
 9.2.50: In Exercises 3550, find the sum of the convergent series.n1 1 9n 2 ...
 9.2.51: In Exercises 5156, (a) write the repeating decimal as a geometric s...
 9.2.52: In Exercises 5156, (a) write the repeating decimal as a geometric s...
 9.2.53: In Exercises 5156, (a) write the repeating decimal as a geometric s...
 9.2.54: In Exercises 5156, (a) write the repeating decimal as a geometric s...
 9.2.55: In Exercises 5156, (a) write the repeating decimal as a geometric s...
 9.2.56: In Exercises 5156, (a) write the repeating decimal as a geometric s...
 9.2.57: In Exercises 5772, determine the convergence or divergence of the s...
 9.2.58: In Exercises 5772, determine the convergence or divergence of the s...
 9.2.59: In Exercises 5772, determine the convergence or divergence of the s...
 9.2.60: In Exercises 5772, determine the convergence or divergence of the s...
 9.2.61: In Exercises 5772, determine the convergence or divergence of the s...
 9.2.62: In Exercises 5772, determine the convergence or divergence of the s...
 9.2.63: In Exercises 5772, determine the convergence or divergence of the s...
 9.2.64: In Exercises 5772, determine the convergence or divergence of the s...
 9.2.65: In Exercises 5772, determine the convergence or divergence of the s...
 9.2.66: In Exercises 5772, determine the convergence or divergence of the s...
 9.2.67: In Exercises 5772, determine the convergence or divergence of the s...
 9.2.68: In Exercises 5772, determine the convergence or divergence of the s...
 9.2.69: In Exercises 5772, determine the convergence or divergence of the s...
 9.2.70: In Exercises 5772, determine the convergence or divergence of the s...
 9.2.71: In Exercises 5772, determine the convergence or divergence of the s...
 9.2.72: In Exercises 5772, determine the convergence or divergence of the s...
 9.2.73: State the definitions of convergent and divergent series.
 9.2.74: Describe the difference between and
 9.2.75: Define a geometric series, state when it converges, and give the fo...
 9.2.76: State the definitions of convergent and divergent series.
 9.2.77: Describe the difference between and
 9.2.78: Define a geometric series, state when it converges, and give the fo...
 9.2.79: In Exercises 7986, find all values of x for which the series conver...
 9.2.80: In Exercises 7986, find all values of x for which the series conver...
 9.2.81: In Exercises 7986, find all values of x for which the series conver...
 9.2.82: In Exercises 7986, find all values of x for which the series conver...
 9.2.83: In Exercises 7986, find all values of x for which the series conver...
 9.2.84: In Exercises 7986, find all values of x for which the series conver...
 9.2.85: In Exercises 7986, find all values of x for which the series conver...
 9.2.86: In Exercises 7986, find all values of x for which the series conver...
 9.2.87: (a) You delete a finite number of terms from a divergent series. Wi...
 9.2.88: Think About It Consider the formula Given and can you conclude that...
 9.2.89: In Exercises 89 and 90, (a) find the common ratio of the geometric ...
 9.2.90: In Exercises 89 and 90, (a) find the common ratio of the geometric ...
 9.2.91: In Exercises 91 and 92, use a graphing utility to graph the functio...
 9.2.92: In Exercises 91 and 92, use a graphing utility to graph the functio...
 9.2.93: Writing In Exercises 93 and 94, use a graphing utility to determine...
 9.2.94: Writing In Exercises 93 and 94, use a graphing utility to determine...
 9.2.95: Marketing An electronic games manufacturer producing a new product ...
 9.2.96: Depreciation A company buys a machine for $225,000 that depreciates...
 9.2.97: Multiplier Effect The annual spending by tourists in a resort city ...
 9.2.98: Multiplier Effect Repeat Exercise 97 if the percent of the revenue ...
 9.2.99: Distance A ball is dropped from a height of 16 feet. Each time it d...
 9.2.100: Time The ball in Exercise 99 takes the following times for each fal...
 9.2.101: Probability In Exercises 101 and 102, the random variable represent...
 9.2.102: Probability In Exercises 101 and 102, the random variable represent...
 9.2.103: Probability A fair coin is tossed repeatedly. The probability that ...
 9.2.104: Probability In an experiment, three people toss a fair coin one at ...
 9.2.105: Area The sides of a square are 16 inches in length. A new square is...
 9.2.106: Length A right triangle is shown above where and Line segments are ...
 9.2.107: In Exercises 107110, use the formula for the partial sum of a geome...
 9.2.108: Sphereflake A sphereflake is a computergenerated fractal that was ...
 9.2.109: Salary You go to work at a company that pays $0.01 for the first da...
 9.2.110: Annuities When an employee receives a paycheck at the end of each m...
 9.2.111: Annuities In Exercises 111114, consider making monthly deposits of ...
 9.2.112: Annuities In Exercises 111114, consider making monthly deposits of ...
 9.2.113: Annuities In Exercises 111114, consider making monthly deposits of ...
 9.2.114: Annuities In Exercises 111114, consider making monthly deposits of ...
 9.2.115: Modeling Data The annual sales (in millions of dollars) for Avon Pr...
 9.2.116: Salary You accept a job that pays a salary of $40,000 for the first...
 9.2.117: True or False? In Exercises 117122, determine whether the statement...
 9.2.118: True or False? In Exercises 117122, determine whether the statement...
 9.2.119: True or False? In Exercises 117122, determine whether the statement...
 9.2.120: True or False? In Exercises 117122, determine whether the statement...
 9.2.121: True or False? In Exercises 117122, determine whether the statement...
 9.2.122: True or False? In Exercises 117122, determine whether the statement...
 9.2.123: Show that the series can be written in the telescoping form where a...
 9.2.124: Let be a convergent series, and let be the remainder of the series ...
 9.2.125: Find two divergent series and such that converges.
 9.2.126: Given two infinite series and such that converges and diverges, pro...
 9.2.127: Suppose that diverges and c is a nonzero constant. Prove that diver...
 9.2.128: If converges where is nonzero, show that diverges
 9.2.129: The Fibonacci sequence is defined recursively by where and (a) Show...
 9.2.130: Find the values of for which the infinite series converges. What is...
 9.2.131: Prove that 1r 1r2 1r3 . . . 1r 1
 9.2.132: Writing The figure below represents an informal way of showing that...
 9.2.133: Writing Read the article The ExponentialDecay Law Applied to Medic...
 9.2.134: Write as a rational number.
 9.2.135: Let be the sum of the first n terms of the sequence 0, 1, 1, 2, 2, ...
Solutions for Chapter 9.2: Series and Convergence
Full solutions for Calculus  8th Edition
ISBN: 9780618502981
Solutions for Chapter 9.2: Series and Convergence
Get Full SolutionsThis textbook survival guide was created for the textbook: Calculus, edition: 8. Chapter 9.2: Series and Convergence includes 135 full stepbystep solutions. This expansive textbook survival guide covers the following chapters and their solutions. Calculus was written by and is associated to the ISBN: 9780618502981. Since 135 problems in chapter 9.2: Series and Convergence have been answered, more than 76579 students have viewed full stepbystep solutions from this chapter.

Blind experiment
An experiment in which subjects do not know if they have been given an active treatment or a placebo

Coefficient matrix
A matrix whose elements are the coefficients in a system of linear equations

Constant function (on an interval)
ƒ(x 1) = ƒ(x 2) x for any x1 and x2 (in the interval)

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

Directed distance
See Polar coordinates.

Independent variable
Variable representing the domain value of a function (usually x).

Line of travel
The path along which an object travels

Logistic growth function
A model of population growth: ƒ1x2 = c 1 + a # bx or ƒ1x2 = c1 + aekx, where a, b, c, and k are positive with b < 1. c is the limit to growth

Main diagonal
The diagonal from the top left to the bottom right of a square matrix

Mathematical model
A mathematical structure that approximates phenomena for the purpose of studying or predicting their behavior

Modified boxplot
A boxplot with the outliers removed.

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.

Pointslope form (of a line)
y  y1 = m1x  x 12.

Powerreducing identity
A trigonometric identity that reduces the power to which the trigonometric functions are raised.

Rational zeros
Zeros of a function that are rational numbers.

Reciprocal of a real number
See Multiplicative inverse of a real number.

Rectangular coordinate system
See Cartesian coordinate system.

Reference angle
See Reference triangle

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

Upper bound for ƒ
Any number B for which ƒ(x) ? B for all x in the domain of ƒ.