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Lesson Example Discussion Quiz: Class Homework

Quiz In Class

Title: Infinite sequence and series

Grade: 1300-a Lesson: S2-L7

Explanation: Hello Students, time to practice and review. Let us take next 10-15 minutes to solve the ten problems using the Quiz Sheet. Then submit the quiz to get the score. This is a good exercise to check your understanding of the concepts.

Quiz: in Class

Problem Id	Problem	Options
1	Compute the sum of the first five terms of the sequence defined by \$a_n = 5n + 1\$.	A) 80 B) 100 C) 90 D) 70
2	Identify the common ratio of the geometric series 5,10,20,40,….	A) 5 B) 2 C) 4 D) 10
3	Write out the first 3 terms of the harmonic series \$ \sum_{n=1}^\infty 1/n \$.	A) 0, 0.5, 0.3231 B) 1, 0.1, 0.3332 C) 1, 0.5, 0.3333 D) 1, 0.2, 0.3114
4	Find the sum of the first 10 terms of the arithmetic series 3,6,9,12,….	A) 160 B) 150 C) 145 D) 165
5	Find the sum of the first 5 terms of the geometric series 2,4,8,16,32,….	A) 43 B) 34 C) 55 D) 62
6	Determine the value of the infinite series: \$1 + (2/7) + (2/7)^2 + (2/7)^3 + ....\$.	A) \$ 7/6 \$ B) \$ 8/5 \$ C) \$ 7/5 \$ D) \$ 8/3 \$
7	Determine whether the sequence \$ a_n= (n^2)/(2^n) \$ converges and find its limit if it does.	A) 1 B) 0 C) 2 D) 3
8	Find the limit of the sequence \$ (1 + (1/n))^n \$ as n to infinity.	A) e B) \$ e^2 \$ C) 0 D) -e
9	Find the sum of the series \$(4) + (2) + (1) + (1/2) + (1/4) + ⋯\$.	A) 6 B) 8 C) 11 D) 13
10	Determine if the series \$ \sum_{n=1}^\infty (-1)^n/(n^2 + 1)\$ converges or diverges.	A) Diverges B) Not diverges C) Converges D) None of these above

Problem Id

Problem

Options

Compute the sum of the first five terms of the sequence defined by \$a_n = 5n + 1\$.

A) 80

B) 100

C) 90

D) 70

Identify the common ratio of the geometric series 5,10,20,40,….

A) 5

B) 2

C) 4

D) 10

Write out the first 3 terms of the harmonic series \$ \sum_{n=1}^\infty 1/n \$.

A) 0, 0.5, 0.3231

B) 1, 0.1, 0.3332

C) 1, 0.5, 0.3333

D) 1, 0.2, 0.3114

Find the sum of the first 10 terms of the arithmetic series 3,6,9,12,….

A) 160

B) 150

C) 145

D) 165

Find the sum of the first 5 terms of the geometric series 2,4,8,16,32,….

A) 43

B) 34

C) 55

D) 62

Determine the value of the infinite series: \$1 + (2/7) + (2/7)^2 + (2/7)^3 + ....\$.

A) \$ 7/6 \$

B) \$ 8/5 \$

C) \$ 7/5 \$

D) \$ 8/3 \$

Determine whether the sequence \$ a_n= (n^2)/(2^n) \$ converges and find its limit if it does.

A) 1

B) 0

C) 2

D) 3

Find the limit of the sequence \$ (1 + (1/n))^n \$ as n to infinity.

A) e

B) \$ e^2 \$

C) 0

D) -e

Find the sum of the series
\$(4) + (2) + (1) + (1/2) + (1/4) + ⋯\$.

A) 6

B) 8

C) 11

D) 13

Determine if the series \$ \sum_{n=1}^\infty (-1)^n/(n^2 + 1)\$ converges or diverges.

A) Diverges

B) Not diverges

C) Converges

D) None of these above