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Sequences and Series Learning Material
Tutorial ID
Title
Tutorial
Video Tutorial
Revision Notes
Revision Questions
12.4
Infinite Series Explained
Infinite Series Explained Revision Questions
1. . What is
1 + 1/4 + 1/16 + 1/64 + ⋯
4/3
5/4
6/5
9/8
Correct Answer: A
2. . What is
1-1/3 - 1/9 - 1/27 + ⋯
4/3
3/4
1/3
1/4
Correct Answer: B
3. . What is
∞∑n = 11/3n
1/2
2/3
3/4
4/5
Correct Answer: B
4. . What can you say about the convergence of the series
∞∑n = 1n2 - 3n + 1/2n + 2
It converges, as L = 0
It converges, as L = 1/2
It diverges
It converges, as L = -1/2
Correct Answer: C
5. . What can you say about the convergence of the series
∞∑n = 1n2 - 1/5n3
It diverges
It converges, as L = 1/5
It converges, as L = -1/5
It converges as L = 0
Correct Answer: A
6. . What kind of series if the following?
∞∑n = 13n/n2
Geometric series
Arithmetic series
Harmonic series
Euler series
Correct Answer: C
7. . What can you say about the convergence of the series
∞∑n = 1(3k/5k - 1)n
It diverges
It converges, as L = 1/5
It converges, as L = -3
It converges, as L = 3/5
Correct Answer: D
8. . What can you say about the convergence of the series
16 + 12 + 8 + …
It converges at 0
It converges at 40
It converges at -40
It diverges
Correct Answer: D
9. . What can you say about the convergence of the series
∞∑n = 15/n!
It cannot be determined
It is convergent as it is an example of a factorial series
It is divergent
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
Convergent, as L = 5
Divergent, as L = 5
Convergent, as L = 5/6
Divergent, as L = 5/6
Correct Answer: B
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