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Lesson Example Discussion Quiz: Class Homework

Quiz At Home

Title: Infinite sequence and series

Grade: 1400-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	Write the fifth term in the sequence defined by \$a_1 = 1,000\$; \$a_n = 1.005a_(n-1) + 1,000 (n > 2)\$.	A) 5044.065 B) 5034.065 C) 5024.065 D) 5134.065
2	Write the fourth term of the sequence defined by \$a_1 = 2; a2 = 3; a_n = 5a_(n-1) - 3a_(n-2) (n get 3)\$.	A) 3 B) 36 C) 153 D) 264
3	Consider the infinite series \$ \sum_{n=1}^\infty (n^3)/(2^n) \$. Determine whether this series converges or diverges; find its sum if it converges.	A) Diverges B) Not converges C) Converges D) None of these above
4	Let \$a_n = (n + 1)/(n^2 + n + 1)\$. Determine whether the sequence \$a_n\$ converges as n approaches infinity. If it converges, find its limit.	A) 3 B) 1 C) Infinity D) 0
5	Evaluate the following series: \$ \sum_{n=1}^\infty (5n + 2)/(7n - 4) \$.	A) Infinity B) \$ 3/5 \$ C) \$ 5/9 \$ D) \$ 5/7 \$
6	Determine if the following series converges or diverges. \$ \sum_{n=0}^\infty ((- 1)^(n - 1))/(6 - 2n)\$.	A) Diverges B) Not converges C) Converges D) None of these above
7	Calculate the sum of the series: \$1 + (3/4) + (3/4)^2 + (3/4)^3 + ... + (3/4)^n\$ as n approaches infinity.	A) 2 B) 4 C) 6 D) 8
8	Evaluate the sum of the series: \$1 + (1/2) + (1/3) + (1/4) + ... + (1/n)\$ as n approaches infinity.	A) Infinity B) 0 C) 1 D) undefined
9	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 \$
10	Determine the Convergence of a Series: \$ \sum_{n=1}^\infty (n^2 + 2n)/(3n^3 + 5)\$.	A) Diverges B) Not converges C) Converges D) None of the above

Problem Id

Problem

Options

Write the fifth term in the sequence defined by \$a_1 = 1,000\$; \$a_n = 1.005a_(n-1) + 1,000 (n > 2)\$.

A) 5044.065

B) 5034.065

C) 5024.065

D) 5134.065

Write the fourth term of the sequence defined by \$a_1 = 2; a2 = 3; a_n = 5a_(n-1) - 3a_(n-2) (n get 3)\$.

A) 3

B) 36

C) 153

D) 264

Consider the infinite series \$ \sum_{n=1}^\infty (n^3)/(2^n) \$. Determine whether this series converges or diverges; find its sum if it converges.

A) Diverges

B) Not converges

C) Converges

D) None of these above

Let \$a_n = (n + 1)/(n^2 + n + 1)\$. Determine whether the sequence \$a_n\$ converges as n approaches infinity. If it converges, find its limit.

A) 3

B) 1

C) Infinity

D) 0

Evaluate the following series: \$ \sum_{n=1}^\infty (5n + 2)/(7n - 4) \$.

A) Infinity

B) \$ 3/5 \$

C) \$ 5/9 \$

D) \$ 5/7 \$

Determine if the following series converges or diverges. \$ \sum_{n=0}^\infty ((- 1)^(n - 1))/(6 - 2n)\$.

A) Diverges

B) Not converges

C) Converges

D) None of these above

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

A) 2

B) 4

C) 6

D) 8

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

A) Infinity

B) 0

C) 1

D) undefined

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 the Convergence of a Series: \$ \sum_{n=1}^\infty (n^2 + 2n)/(3n^3 + 5)\$.

A) Diverges

B) Not converges

C) Converges

D) None of the above