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Lesson Example Discussion Quiz: Class Homework

Quiz In Class

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: in Class

Problem Id	Problem	Options
1	Consider the infinite series \$Σ(n^3)/(2^n)\$, where n ranges from 1 to infinity. Determine whether this series converges or diverges, and if it converges, find its sum.	A) 1 B) \$ 1/2\$ C) 3 D) 2
2	Find the sum of the infinite series \$Σ(n!)/(3^n)\$, where n ranges from 1 to infinity.	A) \$ 5/9 \$ B) Infinity C) \$ 1/2\$ D) 4
3	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) 2 B) 1 C) 0 D) 3
4	Evaluate the following series: \$ \sum_{n=1}^\infty (5n + 2)/(7n - 4) \$	A) \$ 5/9 \$ B) \$ 3/5 \$ C) \$2/5\$ D) None of the above
5	Determine if the following series converges or diverges \$ \sum_{n=0}^\infty (- 1)^(n - 1)/(6 - 2n)\$.	A) None of the above B) Diverges C) Not converges D) Converges
6	Determine if the following series converges or diverges \$ \sum_{n=0}^\infty (- 1)^(n+3)/(n^3+3n+2)\$.	A) Diverges B) Not Converges C) Converges D) None of these above
7	Find the sum of the infinite geometric series with the first term (a) = 3 and the common ratio (r) = 0.5.	A) 5 B) 6 C) 10 D) 16
8	Find the sum of the infinite geometric series \$S = 1 + 0.5 + 0.25 + 0.125 + ...\$.	A) 2 B) 0 C) 1 D) 3
9	Find the sum of the series: 7 + 15 + 23 + 31 + 39 + 47 + ……….. 255.	A) 4392 B) 4192 C) 4291 D) 4128
10	Find the sum of infinite arithmetic series: 10 + 12 + 14 + ….	A) 10 B) - 12 C) - 10 D) 5

Problem Id

Problem

Options

Consider the infinite series \$Σ(n^3)/(2^n)\$, where n ranges from 1 to infinity. Determine whether this series converges or diverges, and if it converges, find its sum.

A) 1

B) \$ 1/2\$

C) 3

D) 2

Find the sum of the infinite series \$Σ(n!)/(3^n)\$, where n ranges from 1 to infinity.

A) \$ 5/9 \$

B) Infinity

C) \$ 1/2\$

D) 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) 2

B) 1

C) 0

D) 3

Evaluate the following series:

\$ \sum_{n=1}^\infty (5n + 2)/(7n - 4) \$

A) \$ 5/9 \$

B) \$ 3/5 \$

C) \$2/5\$

D) None of the above

Determine if the following series converges or diverges

\$ \sum_{n=0}^\infty (- 1)^(n - 1)/(6 - 2n)\$.

A) None of the above

B) Diverges

C) Not converges

D) Converges

Determine if the following series converges or diverges

\$ \sum_{n=0}^\infty (- 1)^(n+3)/(n^3+3n+2)\$.

A) Diverges

B) Not Converges

C) Converges

D) None of these above

Find the sum of the infinite geometric series with the first term (a) = 3 and the common ratio (r) = 0.5.

A) 5

B) 6

C) 10

D) 16

Find the sum of the infinite geometric series
\$S = 1 + 0.5 + 0.25 + 0.125 + ...\$.

A) 2

B) 0

C) 1

D) 3

Find the sum of the series: 7 + 15 + 23 + 31 + 39 + 47 + ……….. 255.

A) 4392

B) 4192

C) 4291

D) 4128

Find the sum of infinite arithmetic series: 10 + 12 + 14 + ….

A) 10

B) - 12

C) - 10

D) 5