Question 1

Write out terms  of the given sequence.

Accepted Answer

,  ,

Question 2

Determine whether  converges or diverges. Show all your work.

Accepted Answer

; the limit does not exist, so the sequence diverges.

Question 3

Determine whether the series converges or diverges. If it converges, find its sum. 
A) 7
B) 
C) 
D) diverges

Accepted Answer

B

Question 4

Show that  is bounded. Show all your work.

Accepted Answer

The answer of Show that  is bounded. Show all...

Question 5

Write a formula that produces the given terms of the sequence.   ,  , 
A) 
B) 
C) 
D)

Accepted Answer

The answer of Write a formula that produces the given...

Question 6

Evaluate the limit. 
A) 9
B) 0
C) 1
D) limit does not exist

Accepted Answer

The answer of Evaluate the limit. 
A) 9
B) 0
C) 1
D)...

Question 7

Determine whether  is increasing, decreasing or neither.
A) decreasing
B) increasing
C) neither

Accepted Answer

The answer of Determine whether  is increasing, decreasing or...

Question 8

Determine whether the sequence converges or diverges. 
A) converges to 0
B) converges to 
C) converges to 
D) diverges

Accepted Answer

The answer of Determine whether the sequence converges or diverges....

Question 9

Find the limit of the sequence  .
A) -7
B) 0
C) 7
D) does not exist

Accepted Answer

The sequence appears to be a constant sequence with value 11, as all the additional characters after 11 do not affect the value of the sequence. Therefore, the limit of the sequence is 11, which is choice B, 0 is incorrect since the sequence is not approaching 0, and choices A and C are incorrect as the sequence does not oscillate or diverge, it remains constant.

Question 10

Find the limit of the sequence. 
A) 1
B) 
C) 7
D) 5

Accepted Answer

The answer of Find the limit of the sequence. 
A)...

Question 11

Determine whether  converges or diverges. Show all your work.

Accepted Answer

The answer of Determine whether  converges or diverges. Show...

Question 12

Determine whether the sequence converges or diverges. 
A) converges to 0
B) converges to 1
C) converges to 
D) diverges

Accepted Answer

Without any knowledge of what the sequence is, we cannot determine the limit of the sequence. However, since the answer choices do not specify any specific limit, we can assume that the sequence either converges to some value or diverges to either positive or negative infinity. Therefore, we cannot rule out any of the first three answer choices. However, since option D is the only choice that indicates divergence, it is the best choice.

Question 13

Determine whether  is increasing, decreasing or neither.
A) decreasing
B) increasing
C) neither

Accepted Answer

The answer of Determine whether  is increasing, decreasing or...

Question 14

Show that  is bounded. Show all your work.

Accepted Answer

The answer of Show that  is bounded. Show all...

Question 15

Write out terms  of the given sequence.

Accepted Answer

The answer of Write out terms  of the given...

Question 16

Determine if  converges or diverges. If convergent, find the sum of the series.
A) converges with sum = 
B) converges with sum = 
C) converges with sum = 
D) diverges

Accepted Answer

The answer of Determine if  converges or diverges. If...

Question 17

Find the limit of the sequence  .
A) 0
B) 9
C) 
D) does not exist

Accepted Answer

The answer of Find the limit of the sequence ...

Question 18

Determine if  converges or diverges. If convergent, find the sum of the series.
A) converges with sum = 
B) converges with sum = 
C) converges with sum = 
D) diverges

Accepted Answer

The answer of Determine if  converges or diverges. If...

Question 19

Determine whether  converges or diverges. Show all your work.

Accepted Answer

The answer of Determine whether  converges or diverges. Show...

Question 20

Write a formula that produces the given terms of the sequence.   ,  ,  , 
A) 
B) 
C) 
D)

Accepted Answer

The answer of Write a formula that produces the given...

Quiz 9: Infinite Series

Write out terms of the given sequence.

Determine whether converges or diverges. Show all your work.

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

Show that is bounded. Show all your work.

Write a formula that produces the given terms of the sequence. , ,

Evaluate the limit.

Determine whether is increasing, decreasing or neither.

Determine whether the sequence converges or diverges.

Find the limit of the sequence .

Find the limit of the sequence.

Determine whether converges or diverges. Show all your work.

Determine whether the sequence converges or diverges.

Determine whether is increasing, decreasing or neither.

Show that is bounded. Show all your work.

Write out terms of the given sequence.

Determine if converges or diverges. If convergent, find the sum of the series.

Find the limit of the sequence .

Determine if converges or diverges. If convergent, find the sum of the series.

Determine whether converges or diverges. Show all your work.

Write a formula that produces the given terms of the sequence. , , ,