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Quiz Discussion

Title: Infinite sequence and series

Grade: 1300-a Lesson: S2-L7

Explanation: Let us discuss a few questions on this topic and review the answers to every question.

Quiz: Discussion in Class

Problem Id	Problem	Options
Steps 1	Find the sum of the infinite geometric series \$S = 4 + 2 + 1 + 1/2 + 1/4 + ...\$.	A) 4 B) 10 C) 8 D) 12
Steps 2	Find the sum of the infinite arithmetic series \$3 + 7 + 11 + 15 + ...\$.	A) Infinity B) 32 C) 46 D) 51
Steps 3	Given an infinite geometric series with the first term (a) equal to 5 and a common ratio (r) equal to \$-1/2\$, find the sum of the series.	A) \$ 13/5 \$ B) \$10/3\$ C) \$ - 7/2 \$ D) \$ 25/3 \$
Steps 4	Find the radius of convergence and the interval of convergence for the power series: \$ \sum_{n=0}^\infty (((-1)^n * x^n) / (2^(n+1)))\$.	A) [- 2, 2] B) [- 3, 3] C) [- 1, 1] D) None of the above
Steps 5	Consider the alternating series: \$ \sum_{n=1}^\infty ((-1)^(n+1) / n^3)\$ Determine whether it converges conditionally or absolutely.	A) Converges conditionally B) Diverges C) Converges absolutely D) None of the above

Problem Id

Problem

Options

Steps 1

Find the sum of the infinite geometric series \$S = 4 + 2 + 1 + 1/2 + 1/4 + ...\$.

A) 4

B) 10

C) 8

D) 12

Find the sum of the infinite arithmetic series \$3 + 7 + 11 + 15 + ...\$.

A) Infinity

B) 32

C) 46

D) 51

Given an infinite geometric series with the first term (a) equal to 5 and a common ratio (r) equal to \$-1/2\$, find the sum of the series.

A) \$ 13/5 \$

B) \$10/3\$

C) \$ - 7/2 \$

D) \$ 25/3 \$

Find the radius of convergence and the interval of convergence for the power series:

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

A) [- 2, 2]

B) [- 3, 3]

C) [- 1, 1]

D) None of the above

Consider the alternating series:

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

Determine whether it converges conditionally or absolutely.

A) Converges conditionally

B) Diverges

C) Converges absolutely

D) None of the above