SaiBook.us SAT-2

Lesson Example Discussion Quiz: Class Homework

Quiz At Home

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: at Home

Problem Id	Problem	Options
1	Find the sum of the series \$ \sum_{n=0}^\infty (-1)^n/ (5)^(n+1) \$.	A) \$ 1/6 \$ B) \$ -1/5 \$ C) \$ -1/4 \$ D) \$ 1/5 \$
2	Determine if the series \$ \sum_{n=1}^\infty ((-1)^n/ n^2) \$ converges or diverges.	A) Diverges B) Converges C) Not diverges D) None of these above
3	Find the sum of the series: 2 + 6 18 + 54 + 162… + 4374.	A) 5550 B) 6500 C) 6,560 D) 6750
4	Find the sum of the infinite geometric series: \$ 3 + 1 + (1/3) + (1/9) + ...\$.	A) 3 B) 3.5 C) 4 D) 4.5
5	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) \$0, 0\$ D) \$-2, 2\$
6	Determine whether the following sequences converge or diverge. If they converge, find the limit. \$ a_n = (1/n) \$.	A) Diverges B) Not diverges C) Converges, and its limit is 0. D) None of these above
7	Find the limit of the following sequences: \$ a_n = (2n^2+3n)/(n^2+1) \$.	A) 1 B) 2 C) 3 D) 4
8	Determine whether the following geometric series converge or diverge. If they converge, find the sum. \$ \sum_{n=1}^\infty 2(1/3)^n \$.	A) Converge, and its sum 3 B) Diverges C) Not diverges D) None of these above
9	Determine whether the following p-series converge or diverge. \$ \sum_{n=1}^\infty (1)/(n^2) \$.	A) Diverges B) Converge C) Not diverges D) None of these above
10	Evaluate the sum of the infinite series: \$S = 1 + 1/8 + 1/27 + 1/64 + 1/125 + ...+1/n^4\$.	A) \$ pi^8/90\$ B) \$ pi^4/80\$ C) \$ pi^4/90\$ D) \$ pi^8/80\$

Problem Id

Problem

Options

Find the sum of the series \$ \sum_{n=0}^\infty (-1)^n/ (5)^(n+1) \$.

A) \$ 1/6 \$

B) \$ -1/5 \$

C) \$ -1/4 \$

D) \$ 1/5 \$

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

A) Diverges

B) Converges

C) Not diverges

D) None of these above

Find the sum of the series: 2 + 6 18 + 54 + 162… + 4374.

A) 5550

B) 6500

C) 6,560

D) 6750

Find the sum of the infinite geometric series: \$ 3 + 1 + (1/3) + (1/9) + ...\$.

A) 3

B) 3.5

C) 4

D) 4.5

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) \$0, 0\$

D) \$-2, 2\$

Determine whether the following sequences converge or diverge. If they converge, find the limit. \$ a_n = (1/n) \$.

A) Diverges

B) Not diverges

C) Converges, and its limit is 0.

D) None of these above

Find the limit of the following sequences: \$ a_n = (2n^2+3n)/(n^2+1) \$.

A) 1

B) 2

C) 3

D) 4

Determine whether the following geometric series converge or diverge. If they converge, find the sum. \$ \sum_{n=1}^\infty 2(1/3)^n \$.

A) Converge, and its sum 3

B) Diverges

C) Not diverges

D) None of these above

Determine whether the following p-series converge or diverge. \$ \sum_{n=1}^\infty (1)/(n^2) \$.

A) Diverges

B) Converge

C) Not diverges

D) None of these above

Evaluate the sum of the infinite series: \$S = 1 + 1/8 + 1/27 + 1/64 + 1/125 + ...+1/n^4\$.

A) \$ pi^8/90\$

B) \$ pi^4/80\$

C) \$ pi^4/90\$

D) \$ pi^8/80\$