 9.1: In Exercises 18, find the sum of the series.3 + 32 +34 +38 + +3210
 9.2: In Exercises 18, find the sum of the series.2+1 12 +14 18 +116
 9.3: In Exercises 18, find the sum of the series.125 + 100 + 80 + + 125(...
 9.4: In Exercises 18, find the sum of the series.(0.5)3 + (0.5)4 + + (0.5)k
 9.5: In Exercises 18, find the sum of the series.b5 + b6 + b7 + b8 + b9 ...
 9.6: In Exercises 18, find the sum of the series.n=413n
 9.7: In Exercises 18, find the sum of the series.20n=413n8
 9.8: In Exercises 18, find the sum of the series.n=03n + 54n
 9.9: In Exercises 912, find the the first four partial sums of thegeomet...
 9.10: In Exercises 912, find the the first four partial sums of thegeomet...
 9.11: In Exercises 912, find the the first four partial sums of thegeomet...
 9.12: In Exercises 912, find the the first four partial sums of thegeomet...
 9.13: In Exercises 1316, does the sequence converge or diverge? Ifa seque...
 9.14: In Exercises 1316, does the sequence converge or diverge? Ifa seque...
 9.15: In Exercises 1316, does the sequence converge or diverge? Ifa seque...
 9.16: In Exercises 1316, does the sequence converge or diverge? Ifa seque...
 9.17: In Exercises 1720, use the integral test to decide whether theserie...
 9.18: In Exercises 1720, use the integral test to decide whether theserie...
 9.19: In Exercises 1720, use the integral test to decide whether theserie...
 9.20: In Exercises 1720, use the integral test to decide whether theserie...
 9.21: In Exercises 2123, use the ratio test to decide if the seriesconver...
 9.22: In Exercises 2123, use the ratio test to decide if the seriesconver...
 9.23: In Exercises 2123, use the ratio test to decide if the seriesconver...
 9.24: In Exercises 2425, use the alternating series test to decidewhether...
 9.25: In Exercises 2425, use the alternating series test to decidewhether...
 9.26: In Exercises 2629, determine whether the series is absolutelyconver...
 9.27: In Exercises 2629, determine whether the series is absolutelyconver...
 9.28: In Exercises 2629, determine whether the series is absolutelyconver...
 9.29: In Exercises 2629, determine whether the series is absolutelyconver...
 9.30: In Exercises 3031, use the comparison test to confirm the statement...
 9.31: In Exercises 3031, use the comparison test to confirm the statement...
 9.32: In Exercises 3235, use the limit comparison test to determinewhethe...
 9.33: In Exercises 3235, use the limit comparison test to determinewhethe...
 9.34: In Exercises 3235, use the limit comparison test to determinewhethe...
 9.35: In Exercises 3235, use the limit comparison test to determinewhethe...
 9.36: In Exercises 3657, determine whether the series converges.+n=11n + 1
 9.37: In Exercises 3657, determine whether the series converges.+n=11n3
 9.38: In Exercises 3657, determine whether the series converges.+n=32n 2
 9.39: In Exercises 3657, determine whether the series converges.+n=1(1)n1...
 9.40: In Exercises 3657, determine whether the series converges.+n=1n2n2 + 1
 9.41: In Exercises 3657, determine whether the series converges.+n=1n2n3 + 1
 9.42: In Exercises 3657, determine whether the series converges.+n=13n(2n)!
 9.43: In Exercises 3657, determine whether the series converges.+n=1(2n)!...
 9.44: In Exercises 3657, determine whether the series converges.+n=1n2 + ...
 9.45: In Exercises 3657, determine whether the series converges.+n=132n(2n)!
 9.46: In Exercises 3657, determine whether the series converges.+n=12n (n...
 9.47: In Exercises 3657, determine whether the series converges.+n=1(1)n ...
 9.48: In Exercises 3657, determine whether the series converges.+n=1(1)n ...
 9.49: In Exercises 3657, determine whether the series converges.+n=02+3n5n
 9.50: In Exercises 3657, determine whether the series converges.+n=11+5n4nn
 9.51: In Exercises 3657, determine whether the series converges.+n=112 + ...
 9.52: In Exercises 3657, determine whether the series converges.+n=31(2n 5)3
 9.53: In Exercises 3657, determine whether the series converges.+n=21n3 3
 9.54: In Exercises 3657, determine whether the series converges.+n=1sin(n...
 9.55: In Exercises 3657, determine whether the series converges.+k=1ln 1 ...
 9.56: In Exercises 3657, determine whether the series converges.+n=1n2n
 9.57: In Exercises 3657, determine whether the series converges.+n=21(ln n)2
 9.58: In Exercises 5861, find the radius of convergence.+n=1(2n)!xn(n!)2
 9.59: In Exercises 5861, find the radius of convergence.+n=0xnn!+1
 9.60: In Exercises 5861, find the radius of convergence.x + 4x2 + 9x3 + 1...
 9.61: In Exercises 5861, find the radius of convergence.x3 +2x25 +3x37 +4...
 9.62: In Exercises 6265, find the interval of convergence.+n=1xn3nn2
 9.63: In Exercises 6265, find the interval of convergence.+n=0(1)n(x 2)n5n
 9.64: In Exercises 6265, find the interval of convergence.+n=1(1)nxnn
 9.65: In Exercises 6265, find the interval of convergence.+n=1xnn!
 9.66: Write the first four terms of the sequence given bysn = (1)n (2n + ...
 9.67: In 6768, find a possible formula for the generalterm of the sequenc...
 9.68: In 6768, find a possible formula for the generalterm of the sequenc...
 9.69: In 6970, let a1 = 5, b1 = 10 and, for n > 1,an = an1 + 2n and bn = ...
 9.70: In 6970, let a1 = 5, b1 = 10 and, for n > 1,an = an1 + 2n and bn = ...
 9.71: For r > 0, how does the convergence of the followingseries depend o...
 9.72: The series *Cn(x 2)n converges when x = 4 anddiverges when x = 6. D...
 9.73: For all the tvalues for which it converges, the function his defin...
 9.74: A $200,000 loan is to be repaid over 20 years in equalmonthly insta...
 9.75: The extraction rate of a mineral is currently 12 milliontons a year...
 9.76: A new car costs $30,000; it loses 10% of its value eachyear. Mainte...
 9.77: 7779 are about bonds, which are issued by a governmentto raise mone...
 9.78: 7779 are about bonds, which are issued by a governmentto raise mone...
 9.79: 7779 are about bonds, which are issued by a governmentto raise mone...
 9.80: Cephalexin is an antibiotic with a halflife in the body of0.9 hour...
 9.81: Before World War I, the British government issued whatare called co...
 9.82: This problem illustrates how banks create credit and canthereby len...
 9.83: Baby formula can contain bacteria which double in numberevery half ...
 9.84: The sequence 1, 5/8, 14/27, 15/32,... is defined by:s1 = 1s2 = 1212...
 9.85: Estimate+n=1(1)n1(2n 1)! to within 0.01 of the actual sumof the ser...
 9.86: Is it possible to construct a convergent alternating series+n=1(1)n...
 9.87: Suppose that 0 bn 2n for all n. Give two examplesof series *bn that...
 9.88: Show that if *an converges and **bn diverges, then(an + bn) diverge...
 9.89: In 8993, the series *an converges with an > 0for all n. Does the se...
 9.90: In 8993, the series *an converges with an > 0for all n. Does the se...
 9.91: In 8993, the series *an converges with an > 0for all n. Does the se...
 9.92: In 8993, the series *an converges with an > 0for all n. Does the se...
 9.93: In 8993, the series *an converges with an > 0for all n. Does the se...
 9.94: Does +n=1 1n +1nconverge or diverge? Does+n=1 1n 1nconverge or dive...
 9.95: This problem shows how you can create a fractal called aCantor Set....
 9.96: Although the harmonic series does not converge, the partialsums gro...
 9.97: Estimate the sum of the first 100,000 terms of the harmonicseries, ...
 9.98: Is the following argument true or false? Give reasons foryour answe...
Solutions for Chapter 9: SEQUENCES AND SERIES
Full solutions for Calculus: Single and Multivariable  6th Edition
ISBN: 9780470888612
Solutions for Chapter 9: SEQUENCES AND SERIES
Get Full SolutionsSince 98 problems in chapter 9: SEQUENCES AND SERIES have been answered, more than 43082 students have viewed full stepbystep solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions. Chapter 9: SEQUENCES AND SERIES includes 98 full stepbystep solutions. Calculus: Single and Multivariable was written by and is associated to the ISBN: 9780470888612. This textbook survival guide was created for the textbook: Calculus: Single and Multivariable , edition: 6.

Definite integral
The definite integral of the function ƒ over [a,b] is Lbaƒ(x) dx = limn: q ani=1 ƒ(xi) ¢x provided the limit of the Riemann sums exists

Distance (in a coordinate plane)
The distance d(P, Q) between P(x, y) and Q(x, y) d(P, Q) = 2(x 1  x 2)2 + (y1  y2)2

Equally likely outcomes
Outcomes of an experiment that have the same probability of occurring.

Fivenumber summary
The minimum, first quartile, median, third quartile, and maximum of a data set.

Frequency
Reciprocal of the period of a sinusoid.

Imaginary part of a complex number
See Complex number.

Limit to growth
See Logistic growth function.

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

Linear inequality in two variables x and y
An inequality that can be written in one of the following forms: y 6 mx + b, y … mx + b, y 7 mx + b, or y Ú mx + b with m Z 0

Logarithmic form
An equation written with logarithms instead of exponents

Modulus
See Absolute value of a complex number.

Number line graph of a linear inequality
The graph of the solutions of a linear inequality (in x) on a number line

Polar equation
An equation in r and ?.

Polar form of a complex number
See Trigonometric form of a complex number.

Quadrantal angle
An angle in standard position whose terminal side lies on an axis.

Quotient of complex numbers
a + bi c + di = ac + bd c2 + d2 + bc  ad c2 + d2 i

Rational numbers
Numbers that can be written as a/b, where a and b are integers, and b ? 0.

Slant line
A line that is neither horizontal nor vertical

Sum of a finite geometric series
Sn = a111  r n 2 1  r

Summation notation
The series a nk=1ak, where n is a natural number ( or ?) is in summation notation and is read "the sum of ak from k = 1 to n(or infinity).” k is the index of summation, and ak is the kth term of the series