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Lesson Example Discussion Quiz: Class Homework

Quiz At Home

Title: Infinite sequence and series

Grade: 10-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: at Home

Problem Id	Problem	Options
1	Determine if the series converges or diverges \$ \sum_{n=1}^\infty 1/((-2)^n(3n-1))\$.	A) Converges B) Not diverges C) Diverges D) None of these above
2	Determine if the series converges or diverges \$ \sum_{n=2}^\infty ((-1)^n(n+1))/(n^2+1) \$.	A) Not Converges B) Converges C) Diverges D) None of these above
3	Find the sum of the series: \$S = 1/2 , 1/4, 1/8, 1/16....\$.	A) 2 B) 3 C) 1 D) 0
4	Determine the value of the infinite series: \$1 + (3/5) + (3/5)^2 + (3/5)^3 + ....\$.	A) \$ 5/9 \$ B) \$ 3/7 \$ C) \$ 4/5 \$ D) \$ 5/2\$
5	Calculate the sum of the series: \$1 + (3/4) + (3/4)^2 + (3/4)^3 + ... + (3/4)^n\$ as n approaches infinity.	A) 1 B) 2 C) 0 D) 4
6	Evaluate the sum of the series: \$1 + (1/2) + (1/3) + (1/4) + ... + (1/n)\$ as n approaches infinity.	A) 1 B) 2 C) Infinity D) 0
7	Evaluate the sum of the infinite series: \$S = 1 + 1/4 + 1/9 + 1/16 + 1/25 + ... + 1/n^2\$.	A) \$ pi/6\$ B) \$ pi^2/6\$ C) \$ pi\$ D) \$ pi/2 \$
8	Determine if the series converges or diverges: \$ \sum_{n=1}^\infty (n^2 + 2n)/(3n^3 + 5)\$.	A) Converges B) Not converges C) Diverges D) None of the above
9	Find the sum of the infinite geometric series with the first term (a) = 7 and the common ratio (r) = \$1/3\$.	A) 1 B) \$ 21/2 \$ C) \$ 63/2 \$ D) 3
10	Find the radius of convergence and the interval of convergence for the power series: \$\sum_{n=0}^\infty ((n + 1) / (2^n)) \$.	A) [- 3, 3] B) [-1/2, 1/2] C) [-2, 2] D) [0, 0]

Problem Id

Problem

Options

Determine if the series converges or diverges
\$ \sum_{n=1}^\infty 1/((-2)^n(3n-1))\$.

A) Converges

B) Not diverges

C) Diverges

D) None of these above

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

A) Not Converges

B) Converges

C) Diverges

D) None of these above

Find the sum of the series:
\$S = 1/2 , 1/4, 1/8, 1/16....\$.

A) 2

B) 3

C) 1

D) 0

Determine the value of the infinite series: \$1 + (3/5) + (3/5)^2 + (3/5)^3 + ....\$.

A) \$ 5/9 \$

B) \$ 3/7 \$

C) \$ 4/5 \$

D) \$ 5/2\$

Calculate the sum of the series:
\$1 + (3/4) + (3/4)^2 + (3/4)^3 + ... + (3/4)^n\$ as n approaches infinity.

A) 1

B) 2

C) 0

D) 4

Evaluate the sum of the series:
\$1 + (1/2) + (1/3) + (1/4) + ... + (1/n)\$ as n approaches infinity.

A) 1

B) 2

C) Infinity

D) 0

Evaluate the sum of the infinite series:
\$S = 1 + 1/4 + 1/9 + 1/16 + 1/25 + ... + 1/n^2\$.

A) \$ pi/6\$

B) \$ pi^2/6\$

C) \$ pi\$

D) \$ pi/2 \$

Determine if the series converges or diverges:
\$ \sum_{n=1}^\infty (n^2 + 2n)/(3n^3 + 5)\$.

A) Converges

B) Not converges

C) Diverges

D) None of the above

Find the sum of the infinite geometric series with the first term (a) = 7 and the common ratio (r) = \$1/3\$.

A) 1

B) \$ 21/2 \$

C) \$ 63/2 \$

D) 3

Find the radius of convergence and the interval of convergence for the power series:
\$\sum_{n=0}^\infty ((n + 1) / (2^n)) \$.

A) [- 3, 3]

B) [-1/2, 1/2]

C) [-2, 2]

D) [0, 0]