Question 1

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

Accepted Answer

A)  1, 3, 2, -1, -3 
B)  1, -3, 4, -5, 6 
C)  1, 3, 2, 1, 0 
D)  1, -1, 2, -3, 5 
A)  1, 3, 2, -1, -3 
B)  1, -3, 4, -5, 6 
C)  1, 3, 2, 1, 0 
D)  1, -1, 2, -3, 5

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. 
-3 -   +   -   + ... +     + ...

Accepted Answer

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

Question 3

A recursion formula and the initial term(s) of a sequence are given. Write out the first five terms of the sequence.
-  = 1,   =   + 5

Accepted Answer

A)  1, 6, 11, 16, 21, 26 
B)  1, 6, 11, 16, 21 
C)  6, 11, 16, 21, 26 
D)  1, 5, 25, 125, 625, 3125 
A)  1, 6, 11, 16, 21, 26 
B)  1, 6, 11, 16, 21 
C)  6, 11, 16, 21, 26 
D)  1, 5, 25, 125, 625, 3125

Question 4

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

Accepted Answer

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

Question 5

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

Accepted Answer

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

Question 6

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

Accepted Answer

A)  diverges 
B)  converges; 1 
C)  converges; 1/3 
D)  converges; 1/2 
A)  diverges 
B)  converges; 1 
C)  converges; 1/3 
D)  converges; 1/2

Question 7

Assume that the sequence converges and find its limit.
-  = -2,   =

Accepted Answer

A)  -6 
B)  8 
C)  -2 
D)  4 
A)  -6 
B)  8 
C)  -2 
D)  4

Question 8

Assume that the sequence converges and find its limit.
-  = 5,   =

Accepted Answer

A)  6 
B)  8 
C)  4 
D)  5 
A)  6 
B)  8 
C)  4 
D)  5

Question 9

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

Accepted Answer

A)  converges; 4 
B)  converges; 3/2 
C)  diverges 
D)  converges; 9/2 
A)  converges; 4 
B)  converges; 3/2 
C)  diverges 
D)  converges; 9/2

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

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

Accepted Answer

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

Question 12

Find a formula for the nth term of the sequence.
-0,   , 0,   , 0 (alternating 0's and   's)

Accepted Answer

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

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. 
-7 + 63 + 567 + ... + 7 .   + ...

Accepted Answer

A)  
  ;   
B)  
  ;   
C)  
  ; series diverges 
D)  
  ; series diverges 
A)  
  ;   
B)  
  ;   
C)  
  ; series diverges 
D)  
  ; series diverges

Question 14

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

Accepted Answer

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

Question 15

Provide an appropriate response. 
-Which of the following is not a condition for applying the integral test to the sequence {   }, where  
I. f(x) is everywhere positive
II. f(x) is decreasing for x $\ge$ N
III. f(x) is continuous for x $\ge$ N

Accepted Answer

A)  III only 
B)  II only 
C)  I only 
D)  All of these are conditions for applying the integral test. 
A)  III only 
B)  II only 
C)  I only 
D)  All of these are conditions for applying the integral test.

Question 16

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

Accepted Answer

A)  Converges conditionally 
B)  converges absolutely 
C)  Diverges 
A)  Converges conditionally 
B)  converges absolutely 
C)  Diverges

Question 17

Determine convergence or divergence of the alternating series.
-

Accepted Answer

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

Question 18

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

Accepted Answer

A)  Converges absolutely 
B)  converges conditionally 
C)  Diverges 
A)  Converges absolutely 
B)  converges conditionally 
C)  Diverges

Question 19

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

Accepted Answer

A)  diverges 
B)  converges absolutely 
C)  converges conditionally 
A)  diverges 
B)  converges absolutely 
C)  converges conditionally

Question 20

Determine convergence or divergence of the alternating series.
-

Accepted Answer

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

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

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

A recursion formula and the initial term(s) of a sequence are given. Write out the first five terms of the sequence. - = 1, = + 5

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

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

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

Assume that the sequence converges and find its limit. - = -2, =

Assume that the sequence converges and find its limit. - = 5, =

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

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

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

Find a formula for the nth term of the sequence. -0, , 0, , 0 (alternating 0's and 's)

Find a formula for the nth partial sum of the series and use it to find the series' sum if the series converges. -7 + 63 + 567 + ... + 7 . + ...

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

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

Determine convergence or divergence of the alternating series. -

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

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

Determine convergence or divergence of the alternating series. -

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

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

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

A recursion formula and the initial term(s) of a sequence are given. Write out the first five terms of the sequence. - = 1, = + 5

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

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

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

Assume that the sequence converges and find its limit. - = -2, =

Assume that the sequence converges and find its limit. - = 5, =

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

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

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

Find a formula for the nth term of the sequence. -0, , 0, , 0 (alternating 0's and 's)

Find a formula for the nth partial sum of the series and use it to find the series' sum if the series converges. -7 + 63 + 567 + ... + 7 . + ...

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

Provide an appropriate response. -Which of the following is not a condition for applying the integral test to the sequence { }, where I. f(x) is everywhere positive II. f(x) is decreasing for x ≥\ge≥ N III. f(x) is continuous for x ≥\ge≥ N

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

Determine convergence or divergence of the alternating series. -

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

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

Determine convergence or divergence of the alternating series. -

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