Deck 9: Section 9: Infinite Series

Question 1

Use the series for to approximate the value of using . Round your answer to three decimal places.

A) 0.125
B) 0.111
C) 0.143
D) 0.100
E) 0.133

Answer 1

0.125

Question 2

Find the sum of the convergent series by using a well-known function. Round your answer to four decimal places.

A) 0.1671
B) 0.7802
C) 2.4061
D) 0.0870
E) 2.3979

Answer 2

0.0870

Question 3

Explain how to use the geometric series to find the series for the function .

A) replace x with
B) replace x with
C) replace x with
D) replace x with
E) replace x with

Answer 3

replace x with

Question 4

Use the power series to determine a power series centered at 0 for the function . .

A)
B)
C)
D)
E)

Question 5

Find a power series for the function centered at 0.

A)
B)
C)
D)
E)

Question 6

Find a geometric power series for the function centered at 0, (i) by the technique shown in Examples 1 and 2 and (ii) by long division.

A)
B)
C)
D)
E)

Question 7

Find a power series for the function centered at 0.

A)
B)
C)
D)
E)

Question 8

Find a power series for the function centered at 0.

A)
B)
C)
D)
E)

Question 9

Identify the interval of convergence of a power series .

A)
B)
C)
D)
E)

Question 10

Find a power series for the function centered at 0.

A)
B)
C)
D)
E)

Question 11

Find a geometric power series for the function centered at 0.

A)
B)
C)
D)
E)

Question 12

Identify the interval of convergence of a power series .

A)
B)
C)
D)
E)

Question 13

Identify the interval of convergence of a power series .

A)
B)
C)
D)
E)

Question 14

Use the power series to determine a power series centered at 0 for the function .

A)
B)
C)
D)
E)

Question 15

Find a geometric power series for the function centered at 0.

A)
B)
C)
D)
E)

Question 16

Explain how to use the geometric series to find the series for the function .

A) replace x with
B) replace x with and multiply the series by
C) replace x with and divide the series by 9
D) replace x with and divide the series by 9
E) replace x with

Question 17

Find the sum of the convergent series by using a well-known function. Round your answer to four decimal places.

A) 0.1419
B) 0.2450
C) 0.8961
D) 0.1651
E) 0.1974

Question 18

Find a power series for the function centered at 1.

A)
B)
C)
D)
E)

Question 19

Use the power series to determine a power series for the function .

A)
B)
C)
D)
E)