Deck 8: Series

Question 1

Approximate by a Taylor polynomial with degree at the number .

A)
B)
C)
D)
E)

Answer 1

Question 2

Find a power series representation for the function and determine the interval of convergence.

A)
B)
C)
D)
E)

Answer 2

Question 3

Find a power series representation for the function and determine the interval of convergence.

A)
B)
C)
D)
E)

Answer 3

Question 4

Find the radius of convergence and the interval of convergence of the power series.

A)
B)
C)
D)

Question 5

Find the Taylor series for centered at the given value of
a. Assume that f has a power series expansion. Also find the associated radius of convergence.

Question 6

Find the Maclaurin series for f (x) using the definition of the Maclaurin series.

A)
B)
C)
D)
E)

Question 7

Find the Maclaurin series for using the definition of a Maclaurin serires.

Question 8

Find the sum of the series.

Question 9

Find a power series representation for the function and determine the interval of convergence.

A)
B)
C)
D)
E)

Question 10

Find a power series representation for the function and determine the radius of convergence.

A)
B)
C)
D)
E)

Question 11

Approximate by a Taylor polynomial with degree at the number .

A)
B)
C)
D)
E)

Question 12

Use series to approximate the definite integral to within the indicated accuracy.

A)0.1447
B)0.0354
C)0.0625
D)0.0125
E)0.2774

Question 13

Evaluate the indefinite integral as an infinite series.

Question 14

Find a power series representation for the function and determine the interval of convergence.

A)
B)
C)
D)
E)

Question 15

Approximate by a Taylor polynomial with degree at the number .

A)
B)
C)
D)
E)

Question 16

Find the interval of convergence of the series.

A)diverges everywhere
B)
C)
D)
E)

Question 17

Use the binomial series to expand the function as a power series. Find the radius of convergence.

Question 18

Find the radius of convergence and the interval of convergence of the power series.

A)
B)
C)
D)

Question 19

Find the Taylor polynomial for the function centered at the number .

A)
B)
C)
D)
E)

Question 20

Use multiplication or division of power series to find the first three nonzero terms in the Maclaurin series for the function.

A)
B)
C)
D)
E)

Question 21

Use the Comparison Test to determine whether the series is convergent or divergent.

Question 22

Determine whether the series is convergent or divergent by expressing as a telescoping sum. If it is convergent, find its sum. .

A)diverges
B)
C)
D)
E)

Question 23

Which of the given series are absolutely convergent?

A)
B)

Question 24

Determine whether the series is convergent or divergent by expressing as a telescoping sum. If it is convergent, find its sum. .

A)
B)diverges
C)
D)
E)

Question 25

Determine whether the series is absolutely convergent, conditionally convergent, or divergent.

A)divergent
B)conditionally convergent
C)absolutely convergent

Question 26

For which positive integers k is the series convergent?

A)
B)
C)
D)
E)

Question 27

Determine whether the given series is convergent or divergent.

Question 28

Determine whether the given series converges or diverges. If it converges, find its sum.

A)
B)Diverges
C)1
D)

Question 29

Determine whether the geometric series converges or diverges. If it converges, find its sum.

A)
B)
C)
D)Diverges

Question 30

Use the Integral Test to determine whether the series is convergent or divergent.

Question 31

Find the radius of convergence and the interval of convergence of the power series.

A)
B)
C)
D)

Question 32

Find all positive values of u for which the series converges.

A)
B)
C)
D)
E)

Question 33

Find the radius of convergence and the interval of convergence of the power series.

Question 34

Use the sum of the first 10 terms to approximate the sum of the series. Estimate the error.

Question 35

Determine whether the series is convergent or divergent.

Question 36

Determine whether the series is absolutely convergent, conditionally convergent, or divergent.

Question 37

Determine whether the given series converges or diverges. If it converges, find its sum.

A)
B)Diverges
C)
D)

Question 38

Determine whether the series is convergent or divergent.

Question 39

Determine whether the series is absolutely convergent, conditionally convergent, or divergent.

A)divergent
B)absolutely convergent
C)conditionally convergent

Question 40

Find the radius of convergence of the series.

A)
B)
C)
D)
E)

Question 41

Determine whether the sequence defined by converges or diverges. If it converges, find its limit.

A)-5
B)Diverges
C)
D)

Question 42

Determine whether the given series converges or diverges. If it converges, find its sum.

Question 43

A right triangle ABC is given with and . CD is drawn perpendicular to AB, DE is drawn perpendicular to BC, EF AB and this process is continued indefinitely as shown in the figure. Find the total length of all the perpendiculars Write your answer to two decimal places.

Question 44

A sequenceis defined recursively by the equation for where . Use your calculator to guess the limit of the sequence.

Question 45

Determine whether the sequence is increasing, decreasing, or not monotonic. Is the sequence bounded?

A)increasing
B)not monotonic
C)decreasing
D)bounded

Question 46

If $600 is invested at interest, compounded annually, then after n years the investment is worth dollars. Find the size of investment after 7 years.

A)$430.21
B)$789.56
C)$1,860.81
D)$1,230.81
E)$1,321.06

Question 47

When money is spent on goods and services, those that receive the money also spend some of it. The people receiving some of the twice-spent money will spend some of that, and so on. Economists call this chain reaction the multiplier effect. In a hypothetical isolated community, the local government begins the process by spending D dollars. Suppose that each recipient of spent money spends and saves of the money that he or she receives. The values c and s are called the marginal propensity to consume and the marginal propensity to save and, of course, .The number k = 1/s is called the multiplier. What is the multiplier if the marginal propensity to consume is ?

A)4
B)6
C)3
D)7
E)2.5

Question 48

Determine whether the sequence defined by converges or diverges. If it converges, find its limit.

A)1
B)Diverges
C)
D)0

Question 49

Determine whether the sequence defined by converges or diverges. If it converges, find its limit.

A)1
B)Diverges
C)0
D)

Question 50

Express the number as a rational number.

Question 51

Express the number as a ratio of integers.