Deck 11: Infinite Sequences and Series

Question 1

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

A) 5, 0, -5, -10, -15
B) 5, -25, 125, -625, 3125
C) -5, 5, -5, 5, -5
D) 5, -5, 5, -5, 5

Answer 1

D

Question 2

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

Answer 2

C

Question 3

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

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

Answer 3

D

Question 4

Write the first four elements of the sequence.

Question 5

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

A) 1, 1, 1, 1, 1
B) 1, 2, 4, 8, 16, 32
C) 1, 2, 4, 8, 16
D) 1, 3, 5, 7, 9

Question 6

Find a formula for the nth term of the sequence.
5, 6, 7, 8, 9 (integers beginning with 5)

Question 7

Write the first four elements of the sequence.

Question 8

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

A) 2, -2, -2, 2, 2
B) 2, -2, 2, -2, 2
C) -2, 2, -2, 2, -2
D) 2, 2, -2, -2, 2

Question 9

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

A) 1, 1, 2, 3, 5
B) 1, 5, 6, 7, 8
C) 1, 5, 6, 12, 18
D) 1, 5, 6, 11, 17

Question 10

Write the first four elements of the sequence.

A) 0, 0, 0, 0
B) 1, 1, 1, 1
C) 0, 1, 0, -1
D) 1, 0, -1, 0

Question 11

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

Question 12

Find a formula for the nth term of the sequence.
-5, -4, -3, -2, -1 (integers beginning with -5)

Question 13

Write the first four elements of the sequence.

Question 14

Find a formula for the nth term of the sequence.

Question 15

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

A) 1, 5, 25, 125, 625
B) 1, 6, 11, 16, 21
C) 5, 6, 7, 8, 9
D) 5, 25, 125, 625, 3125

Question 16

Find a formula for the nth term of the sequence.
, , , 10, 12 (every other integer starting with )

Question 17

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

Question 18

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

Question 19

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

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

Question 20

Write the first four elements of the sequence.

Question 21

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

Question 22

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

Question 23

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

Question 24

Find a formula for the nth term of the sequence.

Question 25

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

Question 26

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

Question 27

Find a formula for the nth term of the sequence.
0, -1, 0, 1, 0, -1, 0, 1 (0, -1, 0, 1 repeated)

Question 28

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

A) 1
B) ln 9
C) 0
D) Diverges

Question 29

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

A) 0
B) 3
C) 1
D) Diverges

Question 30

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

Question 31

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

A) ln 2
B) 1
C) 0
D) Diverges

Question 32

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

Question 33

Find a formula for the nth term of the sequence.
0, 0, 2, 2, 0, 0, 2, 2 (alternating 0's and 2's in pairs)

Question 34

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

A) 0
B) ln 1
C) 1
D) Diverges

Question 35

Find a formula for the nth term of the sequence.
0, 2, 2, 2, 0, 2, 2, 2 (0, 2, 2, 2 repeated)

Question 36

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

Question 37

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

Question 38

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

A) 6
B) 1
C) 0
D) Diverges

Question 39

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

A) 5
B) 4
C) 4.3
D) Diverges

Question 40

Find a formula for the nth term of the sequence.
0, 2, 0, 2, 0 (alternating 0's and 2's)

Question 41

Determine if the sequence is monotonic and if it is bounded.

A) not monotonic; unbounded
B) nondecreasing; bounded
C) decreasing; bounded
D) increasing; unbounded

Question 42

Assume that the sequence converges and find its limit.

A) -3
B) -9
C) 4
D) 8

Question 43

Determine if the sequence is monotonic and if it is bounded.

A) nonincreasing; unbounded
B) not monotonic; unbounded
C) nondecreasing; bounded
D) nondecreasing; unbounded

Question 44

Determine if the sequence is monotonic and if it is bounded.

A) nondecreasing; bounded
B) decreasing; bounded
C) increasing; unbounded
D) not monotonic; bounded

Question 45

Determine whether the nonincreasing sequence converges or diverges.

A) Converges
B) Diverges

Question 46

Determine if the sequence is monotonic and if it is bounded.

A) decreasing; unbounded
B) not monotonic; bounded
C) increasing; bounded
D) nonincreasing; bounded

Question 47

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

A) 1
B) 5
C) 0
D) Diverges

Question 48

Determine if the sequence is monotonic and if it is bounded.

A) decreasing; unbounded
B) nondecreasing; bounded
C) not monotonic; unbounded
D) nondecreasing; unbounded

Question 49

Determine if the sequence is monotonic and if it is bounded.

A) not monotonic; bounded
B) nondecreasing; bounded
C) decreasing; bounded
D) decreasing; unbounded

Question 50

Determine whether the nonincreasing sequence converges or diverges.

A) Converges
B) Diverges

Question 51

Determine whether the nonincreasing sequence converges or diverges.

A) Converges
B) Diverges

Question 52

Determine if the sequence is monotonic and if it is bounded.

A) not monotonic; unbounded
B) nondecreasing; bounded
C) nondecreasing; unbounded
D) increasing; bounded

Question 53

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

Question 54

Assume that the sequence converges and find its limit.

A) 5
B) -5
C) 1
D) 25

Question 55

Determine if the sequence is monotonic and if it is bounded.

A) nondecreasing; bounded
B) not monotonic; bounded
C) increasing; unbounded
D) decreasing; bounded

Question 56

Determine whether the nonincreasing sequence converges or diverges.

A) Diverges
B) Converges

Question 57

Assume that the sequence converges and find its limit.

A) 5
B) 6
C) 7
D) 8

Question 58

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

Question 59

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

A) 6
B) ln 6
C) 0
D) Diverges

Question 60

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

Question 61

Find the smallest value of N that will make the inequality hold for all n > N.

A) 16
B) 15
C) 14
D) 13

Question 62

A) L = ln 2, N = 6
B) L = 0, N = 7
C) L = ln 4, N = 8
D) diverges

Question 63

A) L = 1, N = 28
B) L = 1, N = 6
C) L = 0, N = 28
D) diverges

Question 64

A) L = 1, N = 738
B) L = 1, N = 1549
C) L = 0, N = 1549
D) diverges

Question 65

A) L = ln 2, N = 6
B) L = ln 4, N = 8
C) L = 0, N = 8
D) diverges

Question 66

Find the smallest value of N that will make the inequality hold for all n > N.

A) 25
B) 23
C) 27
D) 20

Question 67

Question 68

Provide an appropriate response.

A) 49
B) 50
C) 2
D) 3

Question 69

Find the smallest value of N that will make the inequality hold for all n > N.

A) 9883
B) 9891
C) 9899
D) 9907

Question 70

Find the smallest value of N that will make the inequality hold for all n > N.

A) 750
B) 731
C) 733
D) 737

Question 71

A) L = 0, N = 37
B) L = 1, N = 28
C) L = 0, N = 28
D) diverges

Question 72

Provide an appropriate response.

Question 73

A) L = 0, N = 13
B) L = 0, N = 10
C) L = 0, N = 8
D) diverges

Question 74

Find the smallest value of N that will make the inequality hold for all n > N.

A) 17
B) 20
C) 18
D) 19

Question 75

Find the smallest value of N that will make the inequality hold for all n > N.

A) 21
B) 31
C) 20
D) 30

Question 76

A) L = 1, N = 394
B) L = 0, N = 237
C) L = 0, N = 394
D) diverges

Question 77

A) L = ln 2, N = 394
B) L = 1, N = 394
C) L = 1, N = 652
D) diverges

Question 78

Question 79

Find the smallest value of N that will make the inequality hold for all n > N.

A) 16
B) 15
C) 17
D) 18

Question 80

Find the smallest value of N that will make the inequality hold for all n > N.

A) 2302
B) 2305
C) 2300
D) 2298