 11.1.1: (a) What is a sequence? (b) What does it mean to say that ? (c) Wha...
 11.1.2: (a) What is a convergent sequence? Give two examples. (b) What is a...
 11.1.3: List the first five terms of the sequence.
 11.1.4: List the first five terms of the sequence.
 11.1.5: List the first five terms of the sequence.
 11.1.6: List the first five terms of the sequence.
 11.1.7: List the first five terms of the sequence.
 11.1.8: List the first five terms of the sequence.
 11.1.9: List the first five terms of the sequence.
 11.1.10: List the first five terms of the sequence.
 11.1.11: List the first five terms of the sequence.
 11.1.12: List the first five terms of the sequence.
 11.1.13: Find a formula for the general term of the sequence, assuming that ...
 11.1.14: Find a formula for the general term of the sequence, assuming that ...
 11.1.15: Find a formula for the general term of the sequence, assuming that ...
 11.1.16: Find a formula for the general term of the sequence, assuming that ...
 11.1.17: Find a formula for the general term of the sequence, assuming that ...
 11.1.18: Find a formula for the general term of the sequence, assuming that ...
 11.1.19: Calculate, to four decimal places, the first ten terms of the seque...
 11.1.20: Calculate, to four decimal places, the first ten terms of the seque...
 11.1.21: Calculate, to four decimal places, the first ten terms of the seque...
 11.1.22: Calculate, to four decimal places, the first ten terms of the seque...
 11.1.23: Determine whether the sequence converges or diverges. If it converg...
 11.1.24: Determine whether the sequence converges or diverges. If it converg...
 11.1.25: Determine whether the sequence converges or diverges. If it converg...
 11.1.26: Determine whether the sequence converges or diverges. If it converg...
 11.1.27: Determine whether the sequence converges or diverges. If it converg...
 11.1.28: Determine whether the sequence converges or diverges. If it converg...
 11.1.29: Determine whether the sequence converges or diverges. If it converg...
 11.1.30: Determine whether the sequence converges or diverges. If it converg...
 11.1.31: Determine whether the sequence converges or diverges. If it converg...
 11.1.32: Determine whether the sequence converges or diverges. If it converg...
 11.1.33: Determine whether the sequence converges or diverges. If it converg...
 11.1.34: Determine whether the sequence converges or diverges. If it converg...
 11.1.35: Determine whether the sequence converges or diverges. If it converg...
 11.1.36: Determine whether the sequence converges or diverges. If it converg...
 11.1.37: Determine whether the sequence converges or diverges. If it converg...
 11.1.38: Determine whether the sequence converges or diverges. If it converg...
 11.1.39: Determine whether the sequence converges or diverges. If it converg...
 11.1.40: Determine whether the sequence converges or diverges. If it converg...
 11.1.41: Determine whether the sequence converges or diverges. If it converg...
 11.1.42: Determine whether the sequence converges or diverges. If it converg...
 11.1.43: Determine whether the sequence converges or diverges. If it converg...
 11.1.44: Determine whether the sequence converges or diverges. If it converg...
 11.1.45: Determine whether the sequence converges or diverges. If it converg...
 11.1.46: Determine whether the sequence converges or diverges. If it converg...
 11.1.47: Determine whether the sequence converges or diverges. If it converg...
 11.1.48: Determine whether the sequence converges or diverges. If it converg...
 11.1.49: Determine whether the sequence converges or diverges. If it converg...
 11.1.50: Determine whether the sequence converges or diverges. If it converg...
 11.1.51: Determine whether the sequence converges or diverges. If it converg...
 11.1.52: Determine whether the sequence converges or diverges. If it converg...
 11.1.53: Determine whether the sequence converges or diverges. If it converg...
 11.1.54: Determine whether the sequence converges or diverges. If it converg...
 11.1.55: Determine whether the sequence converges or diverges. If it converg...
 11.1.56: Determine whether the sequence converges or diverges. If it converg...
 11.1.57: Use a graph of the sequence to decide whether the sequence is conve...
 11.1.58: Use a graph of the sequence to decide whether the sequence is conve...
 11.1.59: Use a graph of the sequence to decide whether the sequence is conve...
 11.1.60: Use a graph of the sequence to decide whether the sequence is conve...
 11.1.61: Use a graph of the sequence to decide whether the sequence is conve...
 11.1.62: Use a graph of the sequence to decide whether the sequence is conve...
 11.1.63: Use a graph of the sequence to decide whether the sequence is conve...
 11.1.64: (a) Determine whether the sequence defined as follows is convergent...
 11.1.65: If $1000 is invested at 6% interest, compounded annually, then afte...
 11.1.66: If you deposit $100 at the end of every month into an account that ...
 11.1.67: A fish farmer has 5000 catfish in his pond. The number of catfish i...
 11.1.68: Find the first 40 terms of the sequence defined by and . Do the sam...
 11.1.69: For what values of is the sequence convergent?
 11.1.70: (a) If is convergent, show that (b) A sequence is defined by and fo...
 11.1.71: Suppose you know that is a decreasing sequence and all its terms li...
 11.1.72: Determine whether the sequence is increasing, decreasing, or not mo...
 11.1.73: Determine whether the sequence is increasing, decreasing, or not mo...
 11.1.74: Determine whether the sequence is increasing, decreasing, or not mo...
 11.1.75: Determine whether the sequence is increasing, decreasing, or not mo...
 11.1.76: Determine whether the sequence is increasing, decreasing, or not mo...
 11.1.77: Determine whether the sequence is increasing, decreasing, or not mo...
 11.1.78: Determine whether the sequence is increasing, decreasing, or not mo...
 11.1.79: Find the limit of the sequence
 11.1.80: A sequence is given by , . (a) By induction or otherwise, show that...
 11.1.81: Show that the sequence defined by is increasing and for all . Deduc...
 11.1.82: Show that the sequence defined by satisfies and is decreasing. Dedu...
 11.1.83: (a) Fibonacci posed the following problem: Suppose that rabbits liv...
 11.1.84: (a) Let , , , . . . , , where is a continuous function. If , show t...
 11.1.85: (a) Use a graph to guess the value of the limit (b) Use a graph of ...
 11.1.86: Use Definition 2 directly to prove that when .
 11.1.87: Prove Theorem 6. [Hint: Use either Definition 2 or the Squeeze Theo...
 11.1.88: Prove Theorem 7.
 11.1.89: Prove that if and is bounded, then .
 11.1.90: Let . (a) Show that if , then (b) Deduce that . (c) Use and in part...
 11.1.91: Let and be positive numbers with . Let be their arithmetic mean and...
 11.1.92: (a) Show that if and , then is convergent and . (b) If and find the...
 11.1.93: The size of an undisturbed fish population has been modeled by the ...
Solutions for Chapter 11.1: INFINITE SEQUENCES AND SERIES
Full solutions for Multivariable Calculus,  7th Edition
ISBN: 9780538497879
Solutions for Chapter 11.1: INFINITE SEQUENCES AND SERIES
Get Full SolutionsChapter 11.1: INFINITE SEQUENCES AND SERIES includes 93 full stepbystep solutions. Since 93 problems in chapter 11.1: INFINITE SEQUENCES AND SERIES have been answered, more than 23712 students have viewed full stepbystep solutions from this chapter. This textbook survival guide was created for the textbook: Multivariable Calculus,, edition: 7. This expansive textbook survival guide covers the following chapters and their solutions. Multivariable Calculus, was written by and is associated to the ISBN: 9780538497879.

Addition property of equality
If u = v and w = z , then u + w = v + z

Common difference
See Arithmetic sequence.

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

Division
a b = aa 1 b b, b Z 0

End behavior asymptote of a rational function
A polynomial that the function approaches as.

Graph of a polar equation
The set of all points in the polar coordinate system corresponding to the ordered pairs (r,?) that are solutions of the polar equation.

Histogram
A graph that visually represents the information in a frequency table using rectangular areas proportional to the frequencies.

Inverse sine function
The function y = sin1 x

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

Multiplication property of equality
If u = v and w = z, then uw = vz

NINT (ƒ(x), x, a, b)
A calculator approximation to ?ab ƒ(x)dx

Reciprocal identity
An identity that equates a trigonometric function with the reciprocal of another trigonometricfunction.

Reduced row echelon form
A matrix in row echelon form with every column that has a leading 1 having 0’s in all other positions.

Semimajor axis
The distance from the center to a vertex of an ellipse.

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

Tangent
The function y = tan x

Triangular number
A number that is a sum of the arithmetic series 1 + 2 + 3 + ... + n for some natural number n.

Trigonometric form of a complex number
r(cos ? + i sin ?)

xintercept
A point that lies on both the graph and the xaxis,.

Xscl
The scale of the tick marks on the xaxis in a viewing window.