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Infinite Series Explained

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Sequences and Series Learning Material
Tutorial IDTitleTutorialVideo
Tutorial		Revision
Notes		Revision
Questions
12.4Infinite Series Explained

Infinite Series Explained Revision Questions

1. . What is

1 + 1/4 + 1/16 + 1/64 + ⋯
  1. 4/3
  2. 5/4
  3. 6/5
  4. 9/8

Correct Answer: A

2. . What is

1-1/3 - 1/9 - 1/27 + ⋯
  1. 4/3
  2. 3/4
  3. 1/3
  4. 1/4

Correct Answer: B

3. . What is

∞∑n = 11/3n
  1. 1/2
  2. 2/3
  3. 3/4
  4. 4/5

Correct Answer: B

4. . What can you say about the convergence of the series

∞∑n = 1n2 - 3n + 1/2n + 2
  1. It converges, as L = 0
  2. It converges, as L = 1/2
  3. It diverges
  4. It converges, as L = -1/2

Correct Answer: C

5. . What can you say about the convergence of the series

∞∑n = 1n2 - 1/5n3
  1. It diverges
  2. It converges, as L = 1/5
  3. It converges, as L = -1/5
  4. It converges as L = 0

Correct Answer: A

6. . What kind of series if the following?

∞∑n = 13n/n2
  1. Geometric series
  2. Arithmetic series
  3. Harmonic series
  4. Euler series

Correct Answer: C

7. . What can you say about the convergence of the series

∞∑n = 1(3k/5k - 1)n
  1. It diverges
  2. It converges, as L = 1/5
  3. It converges, as L = -3
  4. It converges, as L = 3/5

Correct Answer: D

8. . What can you say about the convergence of the series

16 + 12 + 8 + …
  1. It converges at 0
  2. It converges at 40
  3. It converges at -40
  4. It diverges

Correct Answer: D

9. . What can you say about the convergence of the series

∞∑n = 15/n!
  1. It cannot be determined
  2. It is convergent as it is an example of a factorial series
  3. It is divergent
  4. It is an exponential series, so it must be convergent

Correct Answer: B

The root test of the series

∞∑n = 1(5n/n + 6)n

indicates that this series is

  1. Convergent, as L = 5
  2. Divergent, as L = 5
  3. Convergent, as L = 5/6
  4. Divergent, as L = 5/6

Correct Answer: B

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