 11.2.1: . (a) What is the difference between a sequence and a series? (b) W...
 11.2.2: . Explain what it means to say thatn1 an 5
 11.2.3: 34 Calculate the sum of the series whose partial sums are given sn ...
 11.2.4: 34 Calculate the sum of the series whose partial sums are givensn n...
 11.2.5: 58 Calculate the first eight terms of the sequence of partial sums ...
 11.2.6: 58 Calculate the first eight terms of the sequence of partial sums ...
 11.2.7: 58 Calculate the first eight terms of the sequence of partial sums ...
 11.2.8: 58 Calculate the first eight terms of the sequence of partial sums ...
 11.2.9: 914 Find at least 10 partial sums of the series. Graph both the seq...
 11.2.10: 914 Find at least 10 partial sums of the series. Graph both the seq...
 11.2.11: 914 Find at least 10 partial sums of the series. Graph both the seq...
 11.2.12: 914 Find at least 10 partial sums of the series. Graph both the seq...
 11.2.13: 914 Find at least 10 partial sums of the series. Graph both the seq...
 11.2.14: 914 Find at least 10 partial sums of the series. Graph both the seq...
 11.2.15: Let . (a) Determine whether is convergent. (b) Determine whether is...
 11.2.16: . (a) Explain the difference between (b) Explain the difference bet...
 11.2.17: 1726 Determine whether the geometric series is convergent or diverg...
 11.2.18: 1726 Determine whether the geometric series is convergent or diverg...
 11.2.19: 1726 Determine whether the geometric series is convergent or diverg...
 11.2.20: 1726 Determine whether the geometric series is convergent or diverg...
 11.2.21: 1726 Determine whether the geometric series is convergent or diverg...
 11.2.22: 1726 Determine whether the geometric series is convergent or diverg...
 11.2.23: 1726 Determine whether the geometric series is convergent or diverg...
 11.2.24: 1726 Determine whether the geometric series is convergent or diverg...
 11.2.25: 1726 Determine whether the geometric series is convergent or diverg...
 11.2.26: 1726 Determine whether the geometric series is convergent or diverg...
 11.2.27: 27 42 Determine whether the series is convergent or divergent.If it...
 11.2.28: 27 42 Determine whether the series is convergent or divergent.If it...
 11.2.29: 27 42 Determine whether the series is convergent or divergent.If it...
 11.2.30: 27 42 Determine whether the series is convergent or divergent.If it...
 11.2.31: 27 42 Determine whether the series is convergent or divergent.If it...
 11.2.32: 27 42 Determine whether the series is convergent or divergent.If it...
 11.2.33: 27 42 Determine whether the series is convergent or divergent.If it...
 11.2.34: 27 42 Determine whether the series is convergent or divergent.If it...
 11.2.35: 27 42 Determine whether the series is convergent or divergent.If it...
 11.2.36: 27 42 Determine whether the series is convergent or divergent.If it...
 11.2.37: 27 42 Determine whether the series is convergent or divergent.If it...
 11.2.38: 27 42 Determine whether the series is convergent or divergent.If it...
 11.2.39: 27 42 Determine whether the series is convergent or divergent.If it...
 11.2.40: 27 42 Determine whether the series is convergent or divergent.If it...
 11.2.41: 27 42 Determine whether the series is convergent or divergent.If it...
 11.2.42: 27 42 Determine whether the series is convergent or divergent.If it...
 11.2.43: 43 48 Determine whether the series is convergent or divergent by ex...
 11.2.44: 43 48 Determine whether the series is convergent or divergent by ex...
 11.2.45: 43 48 Determine whether the series is convergent or divergent by ex...
 11.2.46: 43 48 Determine whether the series is convergent or divergent by ex...
 11.2.47: 43 48 Determine whether the series is convergent or divergent by ex...
 11.2.48: 43 48 Determine whether the series is convergent or divergent by ex...
 11.2.49: Let (a) Do you think that or ? (b) Sum a geometric series to find t...
 11.2.50: . A sequence of terms is defined by Calculate .
 11.2.51: 5156 Express the number as a ratio of integers.0.8 0.8888 . . . 0
 11.2.52: 5156 Express the number as a ratio of integers.0.46 0.46464646 . . .
 11.2.53: 5156 Express the number as a ratio of integers.2.516 2.516516516 . . .
 11.2.54: 5156 Express the number as a ratio of integers.10.135 10.135353535 ...
 11.2.55: 5156 Express the number as a ratio of integers.1.5342
 11.2.56: 5156 Express the number as a ratio of integers.7.12345
 11.2.57: 5763 Find the values of for which the series converges. Find the su...
 11.2.58: 5763 Find the values of for which the series converges. Find the su...
 11.2.59: 5763 Find the values of for which the series converges. Find the su...
 11.2.60: 5763 Find the values of for which the series converges. Find the su...
 11.2.61: 5763 Find the values of for which the series converges. Find the su...
 11.2.62: 5763 Find the values of for which the series converges. Find the su...
 11.2.63: 5763 Find the values of for which the series converges. Find the su...
 11.2.64: We have seen that the harmonic series is a divergent series whose t...
 11.2.65: 6566 Use the partial fraction command on your CAS to find a conveni...
 11.2.66: 6566 Use the partial fraction command on your CAS to find a conveni...
 11.2.67: If the partial sum of a series is find and
 11.2.68: If the partial sum of a series is , find and
 11.2.69: A patient takes 150 mg of a drug at the same time every day. Just b...
 11.2.70: After injection of a dose of insulin, the concentration of insulin ...
 11.2.71: When money is spent on goods and services, those who receive the mo...
 11.2.72: A certain ball has the property that each time it falls from a heig...
 11.2.73: Find the value of if n21 cn 297909
 11.2.74: Find the value of such that
 11.2.75: In Example 8 we showed that the harmonic series is divergent. Here ...
 11.2.76: Graph the curves , , for on a common screen. By finding the areas b...
 11.2.77: The figure shows two circles and of radius 1 that touch at . is a c...
 11.2.78: A right triangle is given with and . is drawn perpendicular to , is...
 11.2.79: What is wrong with the following calculation? (Guido Ubaldus though...
 11.2.80: Suppose that is known to be a convergent series. Prove that is a di...
 11.2.81: . Prove part (i) of Theorem 8.
 11.2.82: If is divergent and , show that is divergent.
 11.2.83: If is convergent and is divergent, show that the series is divergen...
 11.2.84: If and are both divergent, is necessarily divergent?
 11.2.85: Suppose that a series has positive terms and its partial sums satis...
 11.2.86: The Fibonacci sequence was defined in Section 11.1 by the equations...
 11.2.87: The Cantor set, named after the German mathematician Georg Cantor (...
 11.2.88: (a) A sequence is defined recursively by the equation for , where a...
 11.2.89: Consider the series . (a) Find the partial sums and . Do you recogn...
 11.2.90: In the figure there are infinitely many circles approaching the ver...
Solutions for Chapter 11.2: Series
Full solutions for Calculus: Early Transcendentals  7th Edition
ISBN: 9780538497909
Solutions for Chapter 11.2: Series
Get Full SolutionsCalculus: Early Transcendentals was written by and is associated to the ISBN: 9780538497909. Chapter 11.2: Series includes 90 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. Since 90 problems in chapter 11.2: Series have been answered, more than 31161 students have viewed full stepbystep solutions from this chapter.

artesian coordinate system
An association between the points in a plane and ordered pairs of real numbers; or an association between the points in threedimensional space and ordered triples of real numbers

Compounded continuously
Interest compounded using the formula A = Pert

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

Domain of validity of an identity
The set of values of the variable for which both sides of the identity are defined

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

Fibonacci numbers
The terms of the Fibonacci sequence.

Fibonacci sequence
The sequence 1, 1, 2, 3, 5, 8, 13, . . ..

Halfplane
The graph of the linear inequality y ? ax + b, y > ax + b y ? ax + b, or y < ax + b.

Inductive step
See Mathematical induction.

Inequality
A statement that compares two quantities using an inequality symbol

Mapping
A function viewed as a mapping of the elements of the domain onto the elements of the range

Pseudorandom numbers
Computergenerated numbers that can be used to approximate true randomness in scientific studies. Since they depend on iterative computer algorithms, they are not truly random

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

Right triangle
A triangle with a 90° angle.

Sample survey
A process for gathering data from a subset of a population, usually through direct questioning.

Secant line of ƒ
A line joining two points of the graph of ƒ.

Simple harmonic motion
Motion described by d = a sin wt or d = a cos wt

Standard form of a polar equation of a conic
r = ke 1 e cos ? or r = ke 1 e sin ? ,

Transverse axis
The line segment whose endpoints are the vertices of a hyperbola.

Vector equation for a line in space
The line through P0(x 0, y0, z0) in the direction of the nonzero vector V = <a, b, c> has vector equation r = r0 + tv , where r = <x,y,z>.