Question 1

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

Accepted Answer

A

Question 2

Write out terms  of the given sequence.

Accepted Answer

,  ,

Question 3

Find the limit of the sequence  .
A) 0
B) 8
C) 
D) does not exist

Accepted Answer

A

Question 4

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 5

Write out terms  of the given sequence.

Accepted Answer

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

Question 6

Show that  is bounded. Show all your work.

Accepted Answer

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

Question 7

Determine whether the series converges or diverges. If it converges, find its sum. 
A) 9
B) 
C) 
D) diverges

Accepted Answer

This series is a geometric series with first term 9 and common ratio 3/4. Since the absolute value of the common ratio is less than 1, the series converges, and its sum is given by the formula S = a/(1-r), where a is the first term and r is the common ratio. Plugging in a=9 and r=3/4, we get S = 9/(1-3/4) = 11.

Question 8

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 9

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

Without any information on the terms of the series or the method of summation, we cannot determine whether the series converges or diverges.

Question 10

Find the limit of the sequence. 
A) 1
B) 
C) 7
D) 2

Accepted Answer

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

Question 11

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 12

Find the limit of the sequence  .
A) -4
B) 0
C) 4
D) does not exist

Accepted Answer

The limit of a sequence is the value that the terms of the sequence approach as the index approaches infinity. In this sequence, every term is the same (11eaa88b_90cb_3b6d_a696_311290bc5842_TB5869_11) and does not depend on the index. Therefore, the sequence is constant, and the limit of the sequence is the same constant value (11eaa88b_90cb_3b6d_a696_311290bc5842_TB5869_11) for all values of the index, including as the index approaches infinity. Therefore, the limit of the sequence is the constant value of 11eaa88b_90cb_3b6d_a696_311290bc5842_TB5869_11, which is 0.

Question 13

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

Accepted Answer

The sequence is not given, so we cannot determine whether it converges or diverges.

Question 14

Determine whether  converges or diverges. Show all your work.

Accepted Answer

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

Question 15

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 16

Determine whether  converges or diverges. Show all your work.

Accepted Answer

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

Question 17

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 18

Determine whether  converges or diverges. Show all your work.

Accepted Answer

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

Question 19

Show that  is bounded. Show all your work.

Accepted Answer

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

Question 20

Evaluate the limit. 
A) 10
B) 0
C) 1
D) limit does not exist

Accepted Answer

The answer of Evaluate the limit. 
A) 10
B) 0
C) 1
D)...

Quiz 10: Infinite Series

Determine whether the sequence converges or diverges.

Write out terms of the given sequence.

Find the limit of the sequence .

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

Write out terms of the given sequence.

Show that is bounded. Show all your work.

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

Determine whether is increasing, decreasing or neither.

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.

Find the limit of the sequence .

Determine whether the sequence converges or diverges.

Determine whether converges or diverges. Show all your work.

Determine whether is increasing, decreasing or neither.

Determine whether converges or diverges. Show all your work.

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

Determine whether converges or diverges. Show all your work.

Show that is bounded. Show all your work.

Evaluate the limit.