 11.1.1: . (a) What is a sequence? (b) What does it mean to say that ? (c) W...
 11.1.2: (a) What is a convergent sequence? Give two examples.
 11.1.3: 312 List the first five terms of the sequence.an 2nn2 1a
 11.1.4: 312 List the first five terms of the sequence.an 3n1 2n an
 11.1.5: 312 List the first five terms of the sequence.an 1n15nan
 11.1.6: 312 List the first five terms of the sequence.an cos n2 a
 11.1.7: 312 List the first five terms of the sequence.an 1n 1!a1
 11.1.8: 312 List the first five terms of the sequence.an 1nnn! 1 an
 11.1.9: 312 List the first five terms of the sequence.a1 1 an1 5an 3an
 11.1.10: 312 List the first five terms of the sequence.an1 ann a
 11.1.11: 312 List the first five terms of the sequence.an1 an1 an
 11.1.12: 312 List the first five terms of the sequence.a1 2 a2 1 an1 an an1an
 11.1.13: 1318 Find a formula for the general term of the sequence, assuming ...
 11.1.14: 1318 Find a formula for the general term of the sequence, assuming ...
 11.1.15: 1318 Find a formula for the general term of the sequence, assuming ...
 11.1.16: 1318 Find a formula for the general term of the sequence, assuming ...
 11.1.17: 1318 Find a formula for the general term of the sequence, assuming ...
 11.1.18: 1318 Find a formula for the general term of the sequence, assuming ...
 11.1.19: 1922 Calculate, to four decimal places, the first ten terms of the ...
 11.1.20: 1922 Calculate, to four decimal places, the first ten terms of the ...
 11.1.21: 1922 Calculate, to four decimal places, the first ten terms of the ...
 11.1.22: 1922 Calculate, to four decimal places, the first ten terms of the ...
 11.1.23: 2356 Determine whether the sequence converges or diverges. If it co...
 11.1.24: 2356 Determine whether the sequence converges or diverges. If it co...
 11.1.25: 2356 Determine whether the sequence converges or diverges. If it co...
 11.1.26: 2356 Determine whether the sequence converges or diverges. If it co...
 11.1.27: 2356 Determine whether the sequence converges or diverges. If it co...
 11.1.28: 2356 Determine whether the sequence converges or diverges. If it co...
 11.1.29: 2356 Determine whether the sequence converges or diverges. If it co...
 11.1.30: 2356 Determine whether the sequence converges or diverges. If it co...
 11.1.31: 2356 Determine whether the sequence converges or diverges. If it co...
 11.1.32: 2356 Determine whether the sequence converges or diverges. If it co...
 11.1.33: 2356 Determine whether the sequence converges or diverges. If it co...
 11.1.34: 2356 Determine whether the sequence converges or diverges. If it co...
 11.1.35: 2356 Determine whether the sequence converges or diverges. If it co...
 11.1.36: 2356 Determine whether the sequence converges or diverges. If it co...
 11.1.37: 2356 Determine whether the sequence converges or diverges. If it co...
 11.1.38: 2356 Determine whether the sequence converges or diverges. If it co...
 11.1.39: 2356 Determine whether the sequence converges or diverges. If it co...
 11.1.40: 2356 Determine whether the sequence converges or diverges. If it co...
 11.1.41: 2356 Determine whether the sequence converges or diverges. If it co...
 11.1.42: 2356 Determine whether the sequence converges or diverges. If it co...
 11.1.43: 2356 Determine whether the sequence converges or diverges. If it co...
 11.1.44: 2356 Determine whether the sequence converges or diverges. If it co...
 11.1.45: 2356 Determine whether the sequence converges or diverges. If it co...
 11.1.46: 2356 Determine whether the sequence converges or diverges. If it co...
 11.1.47: 2356 Determine whether the sequence converges or diverges. If it co...
 11.1.48: 2356 Determine whether the sequence converges or diverges. If it co...
 11.1.49: 2356 Determine whether the sequence converges or diverges. If it co...
 11.1.50: 2356 Determine whether the sequence converges or diverges. If it co...
 11.1.51: 2356 Determine whether the sequence converges or diverges. If it co...
 11.1.52: 2356 Determine whether the sequence converges or diverges. If it co...
 11.1.53: 2356 Determine whether the sequence converges or diverges. If it co...
 11.1.54: 2356 Determine whether the sequence converges or diverges. If it co...
 11.1.55: 2356 Determine whether the sequence converges or diverges. If it co...
 11.1.56: 2356 Determine whether the sequence converges or diverges. If it co...
 11.1.57: ; 5763 Use a graph of the sequence to decide whether the sequence i...
 11.1.58: ; 5763 Use a graph of the sequence to decide whether the sequence i...
 11.1.59: ; 5763 Use a graph of the sequence to decide whether the sequence i...
 11.1.60: ; 5763 Use a graph of the sequence to decide whether the sequence i...
 11.1.61: ; 5763 Use a graph of the sequence to decide whether the sequence i...
 11.1.62: ; 5763 Use a graph of the sequence to decide whether the sequence i...
 11.1.63: ; 5763 Use a graph of the sequence to decide whether the sequence i...
 11.1.64: . (a) Determine whether the sequence defined as follows is converge...
 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: 7278 Determine whether the sequence is increasing, decreasing, or n...
 11.1.73: 7278 Determine whether the sequence is increasing, decreasing, or n...
 11.1.74: 7278 Determine whether the sequence is increasing, decreasing, or n...
 11.1.75: 7278 Determine whether the sequence is increasing, decreasing, or n...
 11.1.76: 7278 Determine whether the sequence is increasing, decreasing, or n...
 11.1.77: 7278 Determine whether the sequence is increasing, decreasing, or n...
 11.1.78: 7278 Determine whether the sequence is increasing, decreasing, or n...
 11.1.79: Find the limit of the sequence {s2 , s2s2 , s2s2s2 , . . .}
 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: Sequences
Full solutions for Calculus: Early Transcendentals  7th Edition
ISBN: 9780538497909
Solutions for Chapter 11.1: Sequences
Get Full SolutionsSince 93 problems in chapter 11.1: Sequences have been answered, more than 31078 students have viewed full stepbystep solutions from this chapter. Calculus: Early Transcendentals was written by and is associated to the ISBN: 9780538497909. Chapter 11.1: Sequences includes 93 full stepbystep solutions. This expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: Calculus: Early Transcendentals , edition: 7.

Absolute value of a real number
Denoted by a, represents the number a or the positive number a if a < 0.

Additive inverse of a complex number
The opposite of a + bi, or a  bi

Aphelion
The farthest point from the Sun in a planet’s orbit

Arcsecant function
See Inverse secant function.

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

Average velocity
The change in position divided by the change in time.

Bearing
Measure of the clockwise angle that the line of travel makes with due north

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

Difference of two vectors
<u1, u2>  <v1, v2> = <u1  v1, u2  v2> or <u1, u2, u3>  <v1, v2, v3> = <u1  v1, u2  v2, u3  v3>

Finite series
Sum of a finite number of terms.

Halflife
The amount of time required for half of a radioactive substance to decay.

Product rule of logarithms
ogb 1RS2 = logb R + logb S, R > 0, S > 0,

Projection of u onto v
The vector projv u = au # vƒvƒb2v

Reflection across the xaxis
x, y and (x,y) are reflections of each other across the xaxis.

Right triangle
A triangle with a 90° angle.

Sine
The function y = sin x.

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

Term of a polynomial (function)
An expression of the form anxn in a polynomial (function).

Vertices of an ellipse
The points where the ellipse intersects its focal axis.

Weighted mean
A mean calculated in such a way that some elements of the data set have higher weights (that is, are counted more strongly in determining the mean) than others.