Question 1

Determine convergence or divergence of the series.
-

Accepted Answer

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

Question 2

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)  
  ; 2 
B)  
  ; 2 
C)  
  ; 1 
D)  
  ; 1 
A)  
  ; 2 
B)  
  ; 2 
C)  
  ; 1 
D)  
  ; 1

Question 3

Express the number as the ratio of two integers.
-0.545454 . . .

Accepted Answer

A)  20/37 
B)  6/11 
C)  5 5/11 
D)  2/37 
A)  20/37 
B)  6/11 
C)  5 5/11 
D)  2/37

Question 4

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

Accepted Answer

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

Question 5

Find a formula for the nth term of the sequence.
-6, -6, 6, -6, 6 ( 6's with alternating signs)

Accepted Answer

A)    = 6   
B)    = 6   
C)    = 6   
D)    = 6   
A)    = 6   
B)    = 6   
C)    = 6   
D)    = 6

Question 6

A recursion formula and the initial term(s) of a sequence are given. Write out the first five terms of the sequence.
-  = 1,   =

Accepted Answer

A)  
  
B)  
  
C)  
  
D)  
  
A)  
  
B)  
  
C)  
  
D)

Question 7

Use the integral test to determine whether the series converges.
-

Accepted Answer

A)  diverges 
B)  converges 
A)  diverges 
B)  converges

Question 8

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

Accepted Answer

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

Question 9

Find the sum of the series.
-

Accepted Answer

A)  5/2 
B)  1/2 
C)  1/3 
D)  5/3 
A)  5/2 
B)  1/2 
C)  1/3 
D)  5/3

Question 10

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

Accepted Answer

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

Question 11

A recursion formula and the initial term(s) of a sequence are given. Write out the first five terms of the sequence.
-  = 4,   = -

Accepted Answer

A)  4, -16, 64, -256, 1024 
B)  4, 0, -4, -8, -12 
C)  4, -4, 4, -4, 4 
D)  -4, 4, -4, 4, -4 
A)  4, -16, 64, -256, 1024 
B)  4, 0, -4, -8, -12 
C)  4, -4, 4, -4, 4 
D)  -4, 4, -4, 4, -4

Question 12

Determine convergence or divergence of the series.
-

Accepted Answer

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

Question 13

Determine convergence or divergence of the alternating series.
-

Accepted Answer

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

Question 14

Use the Comparison Test to determine if the series converges or diverges.
-

Accepted Answer

A)  converges 
B)  diverges 
A)  converges 
B)  diverges

Question 15

Find the sum of the series.
-

Accepted Answer

A)  5/6 
B)  - 5/6 
C)  - 1/3 
D)  1/3 
A)  5/6 
B)  - 5/6 
C)  - 1/3 
D)  1/3

Question 16

Find the limit of the sequence if it converges; otherwise indicate divergence.
-  =

Accepted Answer

A)  3 
B)  ±3 
C)  0 
D)  Diverges 
A)  3 
B)  ±3 
C)  0 
D)  Diverges

Question 17

Determine convergence or divergence of the series.
-

Accepted Answer

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

Question 18

Find the limit of the sequence if it converges; otherwise indicate divergence.
-  =

Accepted Answer

A)    
B)    
C)  1 
D)  Diverges 
A)    
B)    
C)  1 
D)  Diverges

Question 19

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

Accepted Answer

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

Question 20

Write the first four elements of the sequence. 
-

Accepted Answer

A)  
  
B)  
  
C)  
  
D)  
  
A)  
  
B)  
  
C)  
  
D)

Determine convergence or divergence of the series. -

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

Express the number as the ratio of two integers. -0.545454 . . .

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

Find a formula for the nth term of the sequence. -6, -6, 6, -6, 6 ( 6's with alternating signs)

A recursion formula and the initial term(s) of a sequence are given. Write out the first five terms of the sequence. - = 1, =

Use the integral test to determine whether the series converges. -

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

Find the sum of the series. -

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

A recursion formula and the initial term(s) of a sequence are given. Write out the first five terms of the sequence. - = 4, = -

Determine convergence or divergence of the series. -

Determine convergence or divergence of the alternating series. -

Use the Comparison Test to determine if the series converges or diverges. -

Find the sum of the series. -

Find the limit of the sequence if it converges; otherwise indicate divergence. - =

Determine convergence or divergence of the series. -

Find the limit of the sequence if it converges; otherwise indicate divergence. - =

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

Write the first four elements of the sequence. -

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 convergence or divergence of the series. -

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

Express the number as the ratio of two integers. -0.545454 . . .

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

Find a formula for the nth term of the sequence. -6, -6, 6, -6, 6 ( 6's with alternating signs)

A recursion formula and the initial term(s) of a sequence are given. Write out the first five terms of the sequence. - = 1, =

Use the integral test to determine whether the series converges. -

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

Find the sum of the series. -

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

A recursion formula and the initial term(s) of a sequence are given. Write out the first five terms of the sequence. - = 4, = -

Determine convergence or divergence of the series. -

Determine convergence or divergence of the alternating series. -

Use the Comparison Test to determine if the series converges or diverges. -

Find the sum of the series. -

Find the limit of the sequence if it converges; otherwise indicate divergence. - =

Determine convergence or divergence of the series. -

Find the limit of the sequence if it converges; otherwise indicate divergence. - =

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

Write the first four elements of the sequence. -

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