Deck 9: Infinite Series

Question 1

The sequence $\left\{ ( - 1 ) ^ { n } \right\}$ is

A)bounded from above only
B)bounded from below only
C)bounded from both above and below
D)decreasing
E)increasing

Answer 1

bounded from both above and below

Question 2

The sequence $\{ 3 n \}$ is

A)bounded from above only
B)bounded from below only
C)bounded from both above and below
D)decreasing
E)not monotonic

Answer 2

bounded from below only

Question 3

The sequence $\left\{ ( - 3 ) ^ { n } \right\}$ is

A)bounded from above only
B)bounded from below only
C)bounded from both above and below
D)decreasing
E)not monotonic

Answer 3

not monotonic

Question 4

The sequence $\{ \sin n \}$ is

A)bounded from above only
B)bounded from below only
C)bounded from both above and below
D)decreasing
E)increasing

Question 5

The limit of the sequence $a _ { n } = \frac { 2 n ^ { 2 } + 4 n - 8 } { n ^ { 2 } - 5 }$ is

A)0
B) $\frac { 1 } { 2 }$
C)1
D)2
E) $\infty$

Question 6

The limit of the sequence $a _ { n } = \frac { - 4 n ^ { 2 } - n - 8 } { 3 n ^ { 2 } + 2 n - 5 }$ is

A)0
B) $- \frac { 4 } { 3 }$
C) $- \frac { 3 } { 4 }$
D) $- \frac { 1 } { 2 }$
E) $\infty$

Question 7

The limit of the sequence $a _ { n } = \frac { 5 n ^ { 2 } - n - 3 } { 9 n ^ { 2 } + 2 n - 7 }$ is

A)0
B) $- \frac { 5 } { 9 }$
C) $\frac { 5 } { 9 }$
D) $- \frac { 1 } { 2 }$
E) $\infty$

Question 8

The limit of the sequence $a _ { n } = \frac { 7 n - 10 } { 5 n ^ { 2 } + 12 n - 7 }$ is

A)0
B) $\frac { 7 } { 5 }$
C) $\frac { 5 } { 7 }$
D) $- \frac { 5 } { 6 }$
E) $\infty$

Question 9

The limit of the sequence $a _ { n } = \frac { n ^ { 3 } - 10 } { 5 n ^ { 2 } + 12 n - 7 }$ is

A)0
B) $\frac { 7 } { 5 }$
C) $\frac { 5 } { 7 }$
D) $- \frac { 5 } { 6 }$
E) $\infty$

Question 10

The limit of the sequence $a _ { n } = e ^ { n + 3 }$ is

A)0
B) $\frac { 7 } { 5 }$
C) $\frac { 5 } { 7 }$
D) $- \frac { 5 } { 6 }$
E) $\infty$

Question 11

The limit of the sequence $a _ { n } = \frac { 3 } { \ln ( n + 2 ) }$ is

A)0
B) $\frac { 7 } { 5 }$
C) $\frac { 5 } { 7 }$
D) $- \frac { 5 } { 6 }$
E) $\infty$

Question 12

The limit of the sequence $a _ { n } = e ^ { - n + 3 }$ is

A)0
B) $\frac { 7 } { 5 }$
C) $\frac { 5 } { 7 }$
D) $- \frac { 5 } { 6 }$
E) $\infty$

Question 13

The limit of the sequence $a _ { n } = \frac { 3 \sqrt { n } + 2 } { \sqrt { n } + 5 }$ is

A)0
B)3
C) $\sqrt { 3 }$
D) $\frac { 2 } { 5 }$
E) $\infty$

Question 14

The limit of the sequence $a _ { n } = \frac { 3 n + 2 } { \sqrt { n } + 5 }$ is

A)0
B)3
C) $\sqrt { 3 }$
D) $\frac { 2 } { 5 }$
E) $\infty$

Question 15

The limit of the sequence $a _ { n } = \frac { 3 n + 8 } { n ^ { 2 } + 5 n - 8 }$ is

A) $0$
B) $3$
C) $\sqrt { 3 }$
D) $\frac { 3 } { 5 }$
E) $\infty$

Question 16

The limit of the sequence $a _ { n } = 1 - \frac { 1 } { e ^ { n } }$ is

A) 0
B)1
C) $- \frac { 1 } { e }$
D) $1 - \frac { 1 } { e }$
E) $\infty$

Question 17

The limit of the sequence $a _ { n } = 5 - | \cos ( n \pi ) |$ is

A)-5
B)5
C)4
D)-4
E)1

Question 18

The limit of the sequence $a _ { n } = 5 - | \sin ( n \pi ) |$ is

A)-5
B)5
C)4
D)-4
E)1

Question 19

The limit of the sequence $a _ { n } = \frac { n } { \ln n }$ is

A)0
B)1
C) $- \frac { 1 } { e }$
D) $1 - \frac { 1 } { e }$
E) $\infty$

Question 20

The limit of the sequence $a _ { n } = \frac { \ln n } { n ^ { 2 } }$ is

A)0
B)1
C) $- \frac { 1 } { e }$
D) $1 - \frac { 1 } { e }$
E) $\infty$

Question 21

Compute the limit of the sequence $\left\{ \left( 1 + \frac { 1 } { n } \right) ^ { 8 n } \right\}$ .

A) $\infty$
B)e
C)8e
D) $e ^ { 8 }$
E)1

Question 22

The sum of the series $\sum _ { n = 1 } ^ { \infty } \left( \frac { 5 } { 2 } \right) ^ { n }$ is

A)0
B)1
C) $\frac { 5 } { 2 }$
D) $\frac { 3 } { 5 }$
E) $\infty$

Question 23

The sum of the series $\sum _ { n = 0 } ^ { \infty } \left( \frac { 3 } { 4 } \right) ^ { n }$ is

A)0
B) $\frac { 1 } { 4 }$
C) $\frac { 3 } { 4 }$
D)4
E) $\infty$

Question 24

The sum of the series $\sum _ { n = 1 } ^ { \infty } \left( \frac { 3 } { 2 } \right) ^ { n }$ is

A)0
B) $\frac { 1 } { 4 }$
C) $\frac { 3 } { 4 }$
D)4
E) $\infty$

Question 25

The sum of the series $\sum _ { n = 1 } ^ { \infty } \cot ^ { n } \left( \frac { \pi } { 4 } \right)$ is

A)0
B)1
C) $\frac { \pi } { 4 }$
D)-1
E) $\infty$

Question 26

The sum of the series $\sum _ { n = 1 } ^ { \infty } \left( \frac { 2 } { e } \right) ^ { n }$ is

A)0
B) $\frac { 2 } { e - 2 }$
C) $\frac { 2 } { 2 - e }$
D) $\frac { e - 2 } { 2 }$
E) $\infty$

Question 27

The sum of the series $\sum _ { n = 1 } ^ { \infty } 1 - \left( \frac { 1 } { 2 } \right) ^ { n }$ is

A)0
B) $\frac { 1 } { 2 }$
C) $- \frac { 1 } { 2 }$
D) $\frac { 3 } { 2 }$
E) $\infty$

Question 28

The sum of the series $\sum _ { n = 1 } ^ { \infty } \frac { 2 ^ { n + 3 } } { 5 ^ { n } }$ is

A) $\frac { 16 } { 3 }$
B) $\frac { 8 } { 3 }$
C) $\frac { 4 } { 3 }$
D) $\frac { 3 } { 2 }$
E) $\infty$

Question 29

The sum of the series $\sum _ { n = 1 } ^ { \infty } \pi ^ { - n }$ is

A) $\pi - 1$
B) $\frac { 1 } { \pi - 1 }$
C) $\pi + 1$
D) $\frac { 1 } { \pi + 1 }$
E) $\infty$

Question 30

The sum of the series $\sum _ { n = 1 } ^ { \infty } \pi ^ { - n }$ is

A)0
B)1
C)-1
D) $\frac { 1 } { 2 }$
E) $\infty$

Question 31

The sum of the series $\sum _ { n = 1 } ^ { \infty } \sec ^ { n } ( 0 )$ is

A)0
B)1
C)-1
D) $\frac { 1 } { 2 }$
E) $\infty$

Question 32

The sum of the series $\sum _ { n = 1 } ^ { \infty } \sin ^ { n } ( 0 )$ is

A)0
B)1
C)-1
D) $\frac { 1 } { 2 }$
E) $\infty$

Question 33

The sum of the series $\sum _ { n = 1 } ^ { \infty } \frac { 1 } { n ( n + 1 ) }$ is

A)0
B) $\frac { 1 } { 2 }$
C) $- \frac { 1 } { 2 }$
D)1
E) $\infty$

Question 34

The sum of the series $\sum _ { n = 2 } ^ { \infty } \frac { 1 } { n ^ { 2 } - 1 }$ is

A)0
B) $\frac { 1 } { 2 }$
C) $\frac { 3 } { 4 }$
D) $\frac { 3 } { 4 }$ .
E) $\infty$

Question 35

The sum of the series $\sum _ { n = 1 } ^ { \infty } \frac { 1 } { ( 2 n - 1 ) ( 2 n + 1 ) }$ is

A)0
B) $\frac { 1 } { 2 }$
C) $- \frac { 1 } { 2 }$
D)1
E) $\infty$

Question 36

The sum of the series $\sum _ { n = 1 } ^ { \infty } \frac { 1 } { ( 3 n + 1 ) ( 3 n - 2 ) }$ is

A)0
B) $\frac { 1 } { 4 }$
C) $\frac { 1 } { 3 }$
D) $\frac { 1 } { 2 }$
E) $\infty$

Question 37

The repeating decimal 0.9999... can be expressed as the rational number

A) $\frac { 89 } { 90 }$
B) $\frac { 899 } { 900 }$
C) $\frac { 8999 } { 9000 }$
D) $\frac { 89,999 } { 90,000 }$
E)1

Question 38

The repeating decimal 0.5555... can be expressed as the rational number

A) $\frac { 5 } { 9 }$
B) $\frac { 49 } { 90 }$
C) $\frac { 499 } { 900 }$
D) $\frac { 4999 } { 9000 }$
E) $\frac { 89,999 } { 90,000 }$

Question 39

The repeating decimal 0.45454545... can be expressed as the rational number

A) $\frac { 5 } { 11 }$
B) $\frac { 49 } { 110 }$
C) $\frac { 499 } { 1100 }$
D) $\frac { 4999 } { 11,000 }$
E) $\frac { 49,999 } { 110,000 }$

Question 40

The repeating decimal 0.87878787... can be expressed as the rational number

A) $\frac { 29 } { 33 }$
B) $\frac { 289 } { 330 }$
C) $\frac { 2899 } { 3300 }$
D) $\frac { 28,999 } { 33,000 }$
E) $\frac { 289,999 } { 330,000 }$

Question 41

Which of the following is true for the infinite series $\sum _ { n = 1 } ^ { \infty } \cos ( n \pi ) ?$

A)Its sequence of partial sums is increasing.
B)Its sequence of partial sums is decreasing.
C) $\lim _ { n \rightarrow \infty } \cos ( n \pi ) = 0$
D)It is convergent.
E)It is divergent.

Question 42

Which of the following is true for the infinite series $\sum _ { n = 1 } ^ { \infty } e ^ { 2 n } ?$

A)Its sequence of partial sums is bounded from above only.
B)Its sequence of partial sums is bounded from both above and below.
C) $\lim _ { n \rightarrow \infty } e ^ { 2 n } = 0$
D)It is convergent.
E)It is divergent.

Question 43

Which of the following is true for the infinite series $\sum _ { n = 1 } ^ { \infty } \sec ( n \pi ) ?$

A)Its sequence of partial sums is increasing.
B)Its sequence of partial sums is decreasing.
C) $\lim _ { n \rightarrow \infty } \sec ( n \pi ) = 0$
D)It is convergent.
E)It is divergent.

Question 44

Which of the following is true for the infinite series $\sum _ { n = 1 } ^ { \infty } \sin ( n \pi ) ?$

A)Its sequence of partial sums is not bounded from below.
B)The terms of its sequence of partial sums are positive.
C) $\lim _ { n \rightarrow \infty } \sin ( n \pi ) \neq 0$
D)It is convergent.
E)It is divergent.

Question 45

Which of the following is true for the infinite series $\sum _ { n = 1 } ^ { \infty } \sin \left( \frac { ( 2 n + 1 ) \pi } { 2 } \right) ?$

A)Its sequence of partial sums is not bounded from below.
B)The terms of its sequence of partial sums are positive.
C) $\lim _ { n \rightarrow \infty } \sin \left( \frac { ( 2 n + 1 ) \pi } { 2 } \right) = 0$
D)It is convergent.
E)It is divergent.

Question 46

Which of the following is true for the infinite series $\sum _ { n = 1 } ^ { \infty } \frac { | \cos ( n \pi ) | } { \sqrt { n + 1 } } ?$

A)Its sequence of partial sums is not bounded from below.
B)Its sequence of partial sums is decreasing.
C) $\lim _ { n \rightarrow \infty } \frac { | \cos ( n \pi ) | } { \sqrt { n + 1 } } \neq 0$
D)It is convergent.
E)It is divergent.

Question 47

Which of the following is true for the infinite series $\overset{ \circ }{a} _ { \cdot } ^ { x } = \frac { 2 } { n ^ { 1 } + 1 } ?$

A)Its sequence of partial sums is not bounded from below.
B)Its sequence of partial sums is decreasing.
C) $\lim _ { n ®¥ } \frac { 1 } { n ^ { 2 } + 1 } ^10$
D)It is convergent.
E)It is divergent.

Question 48

Which of the following is true for the infinite series $\sum _ { n = 2 } ^ { \infty } \frac { 4 } { n ^ { 2 } - 1 } ?$

A)Its sequence of partial sums is not bounded from below.
B)Its sequence of partial sums is decreasing.
C) $\lim _ { n \rightarrow \infty } \frac { 4 } { n ^ { 2 } - 1 } \neq 0$
D)It is convergent.
E)It is divergent.

Question 49

Which of the following is true for the infinite series $\sum _ { n = 1 } ^ { \infty } \frac { 2 n + 5 } { \left( n ^ { 2 } + 5 n \right) ^ { 3 } } ?$

A)Its sequence of partial sums is not bounded from below.
B)Its sequence of partial sums is decreasing.
C) $\lim _ { n \rightarrow \infty } \frac { 2 n + 5 } { \left( n ^ { 2 } + 5 n \right) ^ { 3 } } \neq 0$
D)It is convergent.
E)It is divergent.

Question 50

Which of the following is true for the infinite series $\sum _ { n = 1 } ^ { \infty } \frac { - 3 n } { n ^ { 4 } + 5 } ?$

A)Its sequence of partial sums is not bounded from above.
B)Its sequence of partial sums is increasing.
C) $\lim _ { n \rightarrow \infty } \frac { - 3 n } { n ^ { 4 } + 5 } \neq 0$
D)It is convergent.
E)It is divergent.

Question 51

Which of the following is true for the infinite series $\sum _ { n = 1 } ^ { \infty } e ^ { - n } ?$

A)Its sequence of partial sums is bounded from above.
B)Its sequence of partial sums is decreasing.
C) $\lim _ { x \rightarrow \infty } e ^ { - n } \neq 0$
D)It is convergent.
E)It is divergent.

Question 52

Which of the following is true for the infinite series $\sum _ { n = 1 } ^ { \infty } e ^ { - n } ?$

A)Its sequence of partial sums is not bounded from above.
B)Its sequence of partial sums is decreasing.
C) $\lim _ { x \rightarrow \infty } e ^ { - n } \neq 0$
D)It is convergent.
E)It is divergent.

Question 53

Which of the following is true for the infinite series $\sum _ { n = 1 } ^ { \infty } \pi ^ { - n } ?$

A)Its sequence of partial sums is not bounded from above.
B)Its sequence of partial sums is decreasing.
C) $\lim _ { n \rightarrow \infty } \pi ^ { - n } \neq 0$
D)It is convergent.
E)It is divergent.

Question 54

Which of the following is true for the infinite series $\sum _ { n = 2 } ^ { \infty } \frac { 1 } { 2 n \sqrt { n } } ?$

A)Its sequence of partial sums is not bounded from above.
B)Its sequence of partial sums is decreasing
C) $\lim _ { n \rightarrow \infty } \frac { 1 } { 2 n \sqrt { n } } \neq 0$
D)It is convergent.
E)It is divergent.

Question 55

Which of the following is true for the infinite series $\sum _ { n = 1 } ^ { \infty } n e ^ { - n } ?$

A)Its sequence of partial sums is not bounded from above.
B)Its sequence of partial sums is decreasing.
C) $\lim _ { n \rightarrow \infty } n e ^ { - n } \neq 0$
D)It is convergent.
E)It is divergent.

Question 56

Which of the following is true for the infinite series $\sum _ { n = 1 } ^ { \infty } n ^ { 2 } e ^ { - n ^ { 2 } } ?$

A)Its sequence of partial sums is not bounded from above.
B)Its sequence of partial sums is decreasing.
C) $\lim _ { n \rightarrow \infty } n ^ { 2 } e ^ { - n ^ { 3 } } \neq 0$
D)It is convergent.
E)It is divergent.

Question 57

Which of the following is true for the infinite series $\sum _ { n = 1 } ^ { \infty } \frac { \ln \left( n ^ { 2 } \right) } { n } ?$

A)Its sequence of partial sums is bounded from above.
B)Its sequence of partial sums is decreasing.
C) $\lim _ { n \rightarrow \infty } \frac { \ln \left( n ^ { 2 } \right) } { n } \neq 0$
D)It is convergent.
E)It is divergent.

Question 58

Which of the following is true for the infinite series $\sum _ { n = 1 } ^ { \infty } \sec n ?$

A)Its sequence of partial sums is increasing.
B)Its sequence of partial sums is decreasing.
C) $\lim _ { n \rightarrow \infty } \sec n = 0$
D)It is convergent.
E)It is divergent.

Question 59

Which of the following is true for the infinite series $\sum _ { n = 1 } ^ { \infty } \frac { ( - 1 ) ^ { n } } { 4 ^ { n + 1 } } ?$

A)Its sequence of partial sums is increasing.
B)Its sequence of partial sums is decreasing.
C) $\lim _ { x \rightarrow \infty } \frac { ( - 1 ) ^ { n } } { 4 ^ { n + 1 } } \neq 0$
D)It is convergent.
E)It is divergent.

Question 60

Which of the following is true for the infinite series $\sum _ { n = 1 } ^ { \infty } \frac { n } { 4 ^ { n } } ?$

A)Its sequence of partial sums is not bounded from above.
B)Its sequence of partial sums is decreasing.
C) $\lim _ { n \rightarrow \infty } \frac { n } { 4 ^ { n } } \neq 0$
D)It is convergent.
E)It is divergent.

Question 61

Which of the following is true for the infinite series $\sum _ { n = 1 } ^ { \infty } \frac { 1 } { \ln n } ?$

A)Its sequence of partial sums is bounded from above.
B)Its sequence of partial sums is decreasing.
C) $\lim _ { n \rightarrow \infty } \frac { 1 } { \ln n } = 0$
D)It is convergent.
E)It is divergent.

Question 62

Which of the following is true for the infinite series $\sum _ { n = 1 } ^ { \infty } \frac { 11 } { n ^ { 2 } + 1 } ?$

A)Its sequence of partial sums is not bounded from above.
B)Its sequence of partial sums is decreasing.
C) $\lim _ { n \rightarrow \infty } \frac { 11 } { n ^ { 2 } + 1 } \neq 0$
D)It is convergent.
E)It is divergent.

Question 63

Which of the following is true for the infinite series $\sum _ { n = 1 } ^ { \infty } \frac { 13 } { n ^ { 2 } - 1 } ?$

A)Its sequence of partial sums is not bounded from above.
B)Its sequence of partial sums is decreasing.
C) $\lim _ { n \rightarrow \infty } \frac { 13 } { n ^ { 2 } - 1 } \neq 0$
D)It is convergent.
E)It is divergent.

Question 64

Which of the following is true for the infinite series $\sum _ { n = 1 } ^ { \infty } \frac { 7 } { 2 n - 1 } ?$

A)Its sequence of partial sums is bounded from above.
B)Its sequence of partial sums is decreasing.
C) $\lim _ { n \rightarrow \infty } \frac { 7 } { 2 n - 1 } \neq 0$
D)It is convergent.
E)It is divergent.

Question 65

Which of the following is true for the infinite series $\sum _ { n = 1 } ^ { \infty } \frac { 12 } { e ^ { n } + 1 } ?$

A)Its sequence of partial sums is not bounded from above.
B)Its sequence of partial sums is decreasing.
C) $\lim _ { n \rightarrow \infty } \frac { 12 } { e ^ { n } + 1 } \neq 0$
D)It is convergent.
E)It is divergent.

Question 66

Which of the following is true for the infinite series $\sum _ { n = 1 } ^ { \infty } \frac { 3 } { n ^ { 2 } + n } ?$

A)Its sequence of partial sums is not bounded from above.
B)Its sequence of partial sums is decreasing.
C) $\lim _ { n \rightarrow \infty } \frac { 3 } { n ^ { 2 } + n } \neq 0$
D)It is convergent.
E)It is divergent.

Question 67

Which of the following is true for the infinite series $\sum _ { n = 1 } ^ { \infty } \frac { 8 } { ( n + 1 ) ^ { 2 } } ?$

A)Its sequence of partial sums is not bounded from above.
B)Its sequence of partial sums is decreasing.
C) $\lim _ { n \rightarrow \infty } \frac { 8 } { ( n + 1 ) ^ { 2 } } \neq 0$
D)It is convergent.
E)It is divergent.

Question 68

Which of the following is true for the infinite series $\sum _ { n = 1 } ^ { \infty } \frac { 9 } { n ^ { 2 } + 3 n + 5 } ?$

A)Its sequence of partial sums is not bounded from above.
B)Its sequence of partial sums is decreasing.
C) $\lim _ { n \rightarrow \infty } \frac { 9 } { n ^ { 2 } + 3 n + 5 } \neq 0$
D)It is convergent.
E)It is divergent.

Question 69

Which of the following is true for the infinite series $\sum _ { n = 1 } ^ { \infty } \frac { 22 n } { e ^ { n } - 1 } ?$

A)Its sequence of partial sums is not bounded from above.
B)Its sequence of partial sums is decreasing.
C) $\lim _ { n \rightarrow \infty } \frac { 22 n } { e ^ { n } - 1 } \neq 0$
D)It is convergent.
E)It is divergent.

Question 70

Which of the following is true for the infinite series $\sum _ { n = 1 } ^ { \infty } \frac { 3 } { 3 n - 1 } ?$

A)Its sequence of partial sums is bounded from above.
B)Its sequence of partial sums is decreasing.
C) $\lim _ { n \rightarrow \infty } \frac { 3 } { 3 n - 1 } \neq 0$
D)It is convergent.
E)It is divergent.

Question 71

Which of the following is true for the infinite series $\sum _ { n = 1 } ^ { \infty } \frac { 8 } { 3 n ^ { 2 } - 1 } ?$

A)Its sequence of partial sums is not bounded from above.
B)Its sequence of partial sums is decreasing.
C) $\lim _ { n \rightarrow \infty } \frac { 8 } { 3 n ^ { 2 } - 1 } \neq 0$
D)It is convergent.
E)It is divergent.

Question 72

Which of the following is true for the infinite series $\sum _ { n = 1 } ^ { \infty } \frac { 9 n + 4 } { 3 n ^ { 2 } - 1 } ?$

A)Its sequence of partial sums is bounded from above.
B)Its sequence of partial sums is decreasing.
C) $\lim _ { n \rightarrow \infty } \frac { 9 n + 4 } { 3 n ^ { 2 } - 1 } \neq 0$
D)It is convergent.
E)It is divergent.

Question 73

Which of the following is true for the infinite series $\sum _ { n = 1 } ^ { \infty } \frac { n - 5 } { n ^ { 2 } + 1 } ?$

A)Its sequence of partial sums is bounded from above.
B)Its sequence of partial sums is decreasing.
C) $\lim _ { n \rightarrow \infty } \frac { n - 5 } { n ^ { 2 } + 1 } \neq 0$
D)It is convergent.
E)It is divergent.

Question 74

Which of the following is true for the infinite series $\sum _ { n = 1 } ^ { \infty } \frac { 4 } { 5 ^ { n } - 1 } ?$

A)Its sequence of partial sums is not bounded from above.
B)Its sequence of partial sums is decreasing.
C) $\lim _ { n \rightarrow \infty } \frac { 4 } { 5 ^ { n } - 1 } \neq 0$
D)It is convergent.
E)It is divergent.

Question 75

Which of the following is true for the infinite series $\sum _ { n = 1 } ^ { \infty } \frac { 3 } { 5 ^ { n } - 1 } ?$

A)Its sequence of partial sums is not bounded from above.
B)Its sequence of partial sums is decreasing.
C) $\lim _ { n \rightarrow \infty } \frac { 3 } { 5 ^ { n } - 1 } \neq 0$
D)It is convergent.
E)It is divergent.

Question 76

Which of the following is true for the infinite series $\sum _ { n = 1 } ^ { \infty } - n \pi ^ { 2 } ?$

A)Its sequence of partial sums is bounded from above.
B)Its sequence of partial sums is increasing.
C) $\lim _ { n \rightarrow \infty } n \pi ^ { 2 } = 0$
D)It is convergent.
E)It is divergent.

Question 77

Which of the following is true for the infinite series $\sum _ { n = 1 } ^ { \infty } \frac { \pi ^ { n } } { n ^ { \pi } } ?$

A)Its sequence of partial sums is bounded from above.
B)Its sequence of partial sums is decreasing.
C) $\lim _ { n \rightarrow \infty } \frac { \pi ^ { n } } { n ^ { \pi} } = 0$
D)It is convergent.
E)It is divergent.

Question 78

Which of the following is true for the infinite series $\sum _ { n = 1 } ^ { \infty } \frac { \pi } { n ^ { \pi } } ?$

A)Its sequence of partial sums is not bounded from above.
B)Its sequence of partial sums is decreasing.
C) $\lim _ { n \rightarrow \infty } \frac { \pi } { n ^ { \pi } } \neq 0$
D)It is convergent.
E)It is divergent.

Question 79

Which of the following is true for the infinite series $\sum _ { n = 1 } ^ { \infty } \frac { \pi } { 3 + n ^ { 3 } } ?$

A)Its sequence of partial sums is not bounded from above.
B)Its sequence of partial sums is decreasing.
C) $\lim _ { n \rightarrow \infty } \frac { \pi } { 3 + n ^ { 3 } } \neq 0$
D)It is convergent.
E)It is divergent.

Question 80

Which of the following is true for the infinite series $\sum _ { n = 1 } ^ { \infty } \frac { 4 n } { 3 + 5 n ^ { 2 } } ?$

A)Its sequence of partial sums is bounded from above.
B)Its sequence of partial sums is decreasing.
C) $\lim _ { n \rightarrow \infty } \frac { 4 n } { 3 + 5 n ^ { 2 } } ?$
D)It is convergent.
E)It is divergent.