 8.2.1: (a) What is the difference between a sequence and a series? (b) Wha...
 8.2.2: Explain what it means to say that .
 8.2.3: Find at least 10 partial sums of the series. Graph both the sequenc...
 8.2.4: Find at least 10 partial sums of the series. Graph both the sequenc...
 8.2.5: Find at least 10 partial sums of the series. Graph both the sequenc...
 8.2.6: Find at least 10 partial sums of the series. Graph both the sequenc...
 8.2.7: Find at least 10 partial sums of the series. Graph both the sequenc...
 8.2.8: Find at least 10 partial sums of the series. Graph both the sequenc...
 8.2.9: Let .(a) Determine whether is convergent. (b) Determine whether is ...
 8.2.10: (a) Explain the difference between n j1 ajand (b) Explain the diffe...
 8.2.11: Determine whether the geometric series is convergent or divergent. ...
 8.2.12: Determine whether the geometric series is convergent or divergent. ...
 8.2.13: Determine whether the geometric series is convergent or divergent. ...
 8.2.14: Determine whether the geometric series is convergent or divergent. ...
 8.2.15: Determine whether the geometric series is convergent or divergent. ...
 8.2.16: Determine whether the geometric series is convergent or divergent. ...
 8.2.17: Determine whether the geometric series is convergent or divergent. ...
 8.2.18: Determine whether the geometric series is convergent or divergent. ...
 8.2.19: Determine whether the series is convergent or divergent. If it is c...
 8.2.20: Determine whether the series is convergent or divergent. If it is c...
 8.2.21: Determine whether the series is convergent or divergent. If it is c...
 8.2.22: Determine whether the series is convergent or divergent. If it is c...
 8.2.23: Determine whether the series is convergent or divergent. If it is c...
 8.2.24: Determine whether the series is convergent or divergent. If it is c...
 8.2.25: Determine whether the series is convergent or divergent. If it is c...
 8.2.26: Determine whether the series is convergent or divergent. If it is c...
 8.2.27: Determine whether the series is convergent or divergent. If it is c...
 8.2.28: Determine whether the series is convergent or divergent. If it is c...
 8.2.29: Determine whether the series is convergent or divergent. If it is c...
 8.2.30: Determine whether the series is convergent or divergent. If it is c...
 8.2.31: Determine whether the series is convergent or divergent by expressi...
 8.2.32: Determine whether the series is convergent or divergent by expressi...
 8.2.33: Determine whether the series is convergent or divergent by expressi...
 8.2.34: Determine whether the series is convergent or divergent by expressi...
 8.2.35: Let (a) Do you think that or ? (b) Sum a geometric series to nd the...
 8.2.36: Express the number as a ratio of integers. 0.73 0.73737373...
 8.2.37: Express the number as a ratio of integers. 0.2 0.2222...
 8.2.38: Express the number as a ratio of integers. 6.254 6.2545454 ...
 8.2.39: Express the number as a ratio of integers.
 8.2.40: Express the number as a ratio of integers.
 8.2.41: Find the values of for which the series converges. Find the sum of ...
 8.2.42: Find the values of for which the series converges. Find the sum of ...
 8.2.43: Find the values of for which the series converges. Find the sum of ...
 8.2.44: We have seen that the harmonic series is a divergent series whose t...
 8.2.45: Use the partial fraction command on your CAS to nd a convenient exp...
 8.2.46: Use the partial fraction command on your CAS to nd a convenient exp...
 8.2.47: If the partial sum of a series issn n 1 n 1nd and .
 8.2.48: If the partial sum of a series is , nd and .
 8.2.49: A patient is prescribed a drug and is told to take one 100mg pill ...
 8.2.50: To control an agricultural pest called the medy (Mediterranean frui...
 8.2.51: When money is spent on goods and services, those who receive the mo...
 8.2.52: A certain ball has the property that each time it falls from a heig...
 8.2.53: Find the value of if 1 cn 2
 8.2.54: Find the value of such that enc 10
 8.2.55: In Example 7 we showed that the harmonic series is divergent. Here ...
 8.2.56: Graph the curves , , for on a common screen. By nding the areas bet...
 8.2.57: The gure shows two circles and of radius 1 that touch at . is a com...
 8.2.58: A right triangle is given with and . is drawn perpendicular to , is...
 8.2.59: What is wrong with the following calculation? 0 0 0 0 1 1 1 1 1 1 1...
 8.2.60: Suppose that is known to be a convergent series. Prove that is a di...
 8.2.61: If is convergent and is divergent, show that the series is divergen...
 8.2.62: If and are both divergent, is necessarily divergent?
 8.2.63: Suppose that a series has positive terms and its partial sums satis...
 8.2.64: The Fibonacci sequence was dened in Section 8.1 by the equationsSho...
 8.2.65: The Cantor set, named after the German mathematician Georg Cantor (...
 8.2.66: (a) A sequence is dened recursively by the equation for , where and...
 8.2.67: Consider the series . (a) Find the partial sums and . Do you recogn...
 8.2.68: In the gure there are innitely many circles approaching the vertice...
Solutions for Chapter 8.2: SERIES
Full solutions for Single Variable Calculus: Concepts and Contexts (Stewart's Calculus Series)  4th Edition
ISBN: 9780495559726
Solutions for Chapter 8.2: SERIES
Get Full SolutionsSingle Variable Calculus: Concepts and Contexts (Stewart's Calculus Series) was written by and is associated to the ISBN: 9780495559726. 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 68 problems in chapter 8.2: SERIES have been answered, more than 20130 students have viewed full stepbystep solutions from this chapter. Chapter 8.2: SERIES includes 68 full stepbystep solutions.

Algebraic model
An equation that relates variable quantities associated with phenomena being studied

Conic section (or conic)
A curve obtained by intersecting a doublenapped right circular cone with a plane

Conjugate axis of a hyperbola
The line segment of length 2b that is perpendicular to the focal axis and has the center of the hyperbola as its midpoint

Constant of variation
See Power function.

Cycloid
The graph of the parametric equations

Difference of functions
(ƒ  g)(x) = ƒ(x)  g(x)

Doubleblind experiment
A blind experiment in which the researcher gathering data from the subjects is not told which subjects have received which treatment

Exponential growth function
Growth modeled by ƒ(x) = a ? b a > 0, b > 1 .

Higherdegree polynomial function
A polynomial function whose degree is ? 3

Horizontal Line Test
A test for determining whether the inverse of a relation is a function.

Imaginary part of a complex number
See Complex number.

Implicitly defined function
A function that is a subset of a relation defined by an equation in x and y.

Lower bound for real zeros
A number c is a lower bound for the set of real zeros of ƒ if ƒ(x) Z 0 whenever x < c

Magnitude of an arrow
The magnitude of PQ is the distance between P and Q

Parametric equations
Equations of the form x = ƒ(t) and y = g(t) for all t in an interval I. The variable t is the parameter and I is the parameter interval.

Positive linear correlation
See Linear correlation.

Product of functions
(ƒg)(x) = ƒ(x)g(x)

Row echelon form
A matrix in which rows consisting of all 0’s occur only at the bottom of the matrix, the first nonzero entry in any row with nonzero entries is 1, and the leading 1’s move to the right as we move down the rows.

Slopeintercept form (of a line)
y = mx + b

Variation
See Power function.