Question 1

Determine if the geometric series converges or diverges. If it converges, find its sum.
-1 + ( -9) +   +   +   + . . .

Accepted Answer

A)  converges, 9 
B)  converges, 81 
C)  diverges 
D)  converges, 90 
A)  converges, 9 
B)  converges, 81 
C)  diverges 
D)  converges, 90

Question 2

Determine if the series converges absolutely, converges, or diverges.
-

Accepted Answer

A)  diverges 
B)  Converges conditionally 
C)  Converges absolutely 
A)  diverges 
B)  Converges conditionally 
C)  Converges absolutely

Question 3

Find a formula for the nth partial sum of the series and use it to find the series' sum if the series converges. 
-3 +   +   + ... +   + ...

Accepted Answer

A)  
  ; 4 
B)  
  ;   
C)  
  ;   
D)  
  ; 4 
A)  
  ; 4 
B)  
  ;   
C)  
  ;   
D)  
  ; 4

Question 4

Find the limit of the sequence or determine that the sequence diverges.
-

Accepted Answer

A)  7 
B)  The sequence diverges. 
C)  - 7 
D)  0 
A)  7 
B)  The sequence diverges. 
C)  - 7 
D)  0

Question 5

Use the root test to determine if the series converges or diverges.
-

Accepted Answer

A)  Converges 
B)  Diverges 
A)  Converges 
B)  Diverges

Question 6

Find the limit of the sequence or determine that the limit does not exist.
-  =

Accepted Answer

A)  ln 7 
B)  does not exist 
C)    
D)  0 
A)  ln 7 
B)  does not exist 
C)    
D)  0

Question 7

Express the number as the ratio of two integers.
-0.562562 . . .

Accepted Answer

A)  562/99 
B)  5620/99 
C)  562/999 
D)  5620/999 
A)  562/99 
B)  5620/99 
C)  562/999 
D)  5620/999

Question 8

Use the root test to determine if the series converges or diverges.
-

Accepted Answer

A)  Converges 
B)  Diverges 
A)  Converges 
B)  Diverges

Question 9

Solve the problem.
-A company adopts an advertising campaign to weekly add to its customer base. It assumes that as an average fifty percent of its new customers, those added the previous week, will bring in one friend, but those who have been customers longer will not be very effective as recruiters and can be discounted. A media campaign brings in 10,000 customers initially. What is the expected total number of customers with whom the company can expect to have dealings?

Accepted Answer

A)  The sum diverges to infinity. 
B)  30,000 customers 
C)  20,000 customers 
D)  15,000 customers 
A)  The sum diverges to infinity. 
B)  30,000 customers 
C)  20,000 customers 
D)  15,000 customers

Question 10

Determine if the series converges or diverges. If the series converges, find its sum.
-

Accepted Answer

A)  diverges 
B)  converges;   
C)  converges;   
D)  converges;   
A)  diverges 
B)  converges;   
C)  converges;   
D)  converges;

Question 11

Express the number as the ratio of two integers.
-0.747474 . . .

Accepted Answer

A)  74/99 
B)  20/27 
C)  740/99 
D)  2/27 
A)  74/99 
B)  20/27 
C)  740/99 
D)  2/27

Question 12

Use the ratio test to determine if the series converges or diverges.
-

Accepted Answer

A)  Converges 
B)  Diverges 
A)  Converges 
B)  Diverges

Question 13

Find a formula for the nth partial sum of the series and use it to find the series' sum if the series converges. 
-  +   +   + ... +   + ...

Accepted Answer

A)  
  ; 3 
B)  
  ; 3 
C)  
  ;   
D)  
  ;   
A)  
  ; 3 
B)  
  ; 3 
C)  
  ;   
D)  
  ;

Question 14

Determine if the series converges or diverges. If the series converges, find its sum.
-

Accepted Answer

A)  converges;   
B)  converges;   
C)  diverges 
D)  converges; 1 
A)  converges;   
B)  converges;   
C)  diverges 
D)  converges; 1

Question 15

Determine convergence or divergence of the series.
-

Accepted Answer

A)  Converges 
B)  Diverges 
A)  Converges 
B)  Diverges

Question 16

Find the limit of the sequence or determine that the limit does not exist.
-  =

Accepted Answer

A)  does not exist 
B)  ln 3 
C)  0 
D)  1 
A)  does not exist 
B)  ln 3 
C)  0 
D)  1

Question 17

Find the limit of the sequence or determine that the limit does not exist.
-  =

Accepted Answer

A)  1 
B)  ln 6 
C)  0 
D)  does not exist 
A)  1 
B)  ln 6 
C)  0 
D)  does not exist

Question 18

Express the number as the ratio of two integers.
-0.5303030 . . .

Accepted Answer

A)  175/33 
B)  35/22 
C)  35/66 
D)  35/33 
A)  175/33 
B)  35/22 
C)  35/66 
D)  35/33

Question 19

Determine convergence or divergence of the alternating series.
-

Accepted Answer

A)  Diverges 
B)  Converges 
A)  Diverges 
B)  Converges

Question 20

Find the infinite sum accurate to three decimal places.
-

Accepted Answer

A)  0.460 
B)  -0.320 
C)  0.859 
D)  -0.859 
A)  0.460 
B)  -0.320 
C)  0.859 
D)  -0.859

Determine if the geometric series converges or diverges. If it converges, find its sum. -1 + ( -9) + + + + . . .

Determine if the series converges absolutely, converges, or diverges. -

Find a formula for the nth partial sum of the series and use it to find the series' sum if the series converges. -3 + + + ... + + ...

Find the limit of the sequence or determine that the sequence diverges. -

Use the root test to determine if the series converges or diverges. -

Find the limit of the sequence or determine that the limit does not exist. - =

Express the number as the ratio of two integers. -0.562562 . . .

Use the root test to determine if the series converges or diverges. -

Determine if the series converges or diverges. If the series converges, find its sum. -

Express the number as the ratio of two integers. -0.747474 . . .

Use the ratio test to determine if the series converges or diverges. -

Find a formula for the nth partial sum of the series and use it to find the series' sum if the series converges. - + + + ... + + ...

Determine if the series converges or diverges. If the series converges, find its sum. -

Determine convergence or divergence of the series. -

Find the limit of the sequence or determine that the limit does not exist. - =

Find the limit of the sequence or determine that the limit does not exist. - =

Express the number as the ratio of two integers. -0.5303030 . . .

Determine convergence or divergence of the alternating series. -

Find the infinite sum accurate to three decimal places. -

Functions

Limits

Derivatives

Applications of the Derivative

Integration

Applications of Integration

Logarithmic, Exponential, and Hyperbolic Functions

Integration Techniques

Differential Equations

Power Series

Parametric and Polar Curves

Vectors and the Geometry of Space

Vector-Valued Functions

Functions of Several Variables

Multiple Integration

Vector Calculus

Filters

Exam 10: Sequences and Infinite Series

Determine if the geometric series converges or diverges. If it converges, find its sum. -1 + ( -9) + + + + . . .

Determine if the series converges absolutely, converges, or diverges. -

Find a formula for the nth partial sum of the series and use it to find the series' sum if the series converges. -3 + + + ... + + ...

Find the limit of the sequence or determine that the sequence diverges. -

Use the root test to determine if the series converges or diverges. -

Find the limit of the sequence or determine that the limit does not exist. - =

Express the number as the ratio of two integers. -0.562562 . . .

Use the root test to determine if the series converges or diverges. -

Determine if the series converges or diverges. If the series converges, find its sum. -

Express the number as the ratio of two integers. -0.747474 . . .

Use the ratio test to determine if the series converges or diverges. -

Find a formula for the nth partial sum of the series and use it to find the series' sum if the series converges. - + + + ... + + ...

Determine if the series converges or diverges. If the series converges, find its sum. -

Determine convergence or divergence of the series. -

Find the limit of the sequence or determine that the limit does not exist. - =

Find the limit of the sequence or determine that the limit does not exist. - =

Express the number as the ratio of two integers. -0.5303030 . . .

Determine convergence or divergence of the alternating series. -

Find the infinite sum accurate to three decimal places. -

Functions

Limits

Derivatives

Applications of the Derivative

Integration

Applications of Integration

Logarithmic, Exponential, and Hyperbolic Functions

Integration Techniques

Differential Equations

Power Series

Parametric and Polar Curves

Vectors and the Geometry of Space

Vector-Valued Functions

Functions of Several Variables

Multiple Integration

Vector Calculus

Filters