For each of the series below select the letter from a to c that best applies and the letter from d to k that best applies. A possible answer is af, for example. A. The series is absolutely convergent. B. The series converges, but not absolutely. C. The series diverges. D. The alternating series test shows the series converges. E. The series is a p-series. F. The series is a geometric series. G. We can decide whether this series converges by comparison with a p series. H. We can decide whether this series converges by comparison with a geometric series. I. Partial sums of the series telescope. J. The terms of the series do not have limit zero. K. None of the above reasons applies to the convergence or divergence of the series. 00 7 + sin(n) 1. Vn (2n + 4)! (n!)2 cos (nx) 2. 00 cos(nn) 4. 1 5. 1 6. n log(5 + n)
For each of the series below select the letter from a to c that best applies and the letter from d to k that best applies. A possible answer is af, for example. A. The series is absolutely convergent. B. The series converges, but not absolutely. C. The series diverges. D. The alternating series test shows the series converges. E. The series is a p-series. F. The series is a geometric series. G. We can decide whether this series converges by comparison with a p series. H. We can decide whether this series converges by comparison with a geometric series. I. Partial sums of the series telescope. J. The terms of the series do not have limit zero. K. None of the above reasons applies to the convergence or divergence of the series. 00 7 + sin(n) 1. Vn (2n + 4)! (n!)2 cos (nx) 2. 00 cos(nn) 4. 1 5. 1 6. n log(5 + n)
Chapter9: Sequences, Probability And Counting Theory
Section: Chapter Questions
Problem 13PT: Use the formula for the sum of the first n terms of a geometric series to find k=170.2(5)k1 .
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For each of the series below select the letter from a to c that best applies and the letter from d to k that best applies. A possible answer is af, for example.
A. The series is absolutely convergent.
B. The series converges, but not absolutely.
C. The series diverges.
D. The alternating series test shows the series converges.
E. The series is a p-series.
F. The series is a geometric series.
G. We can decide whether this series converges by comparison with a p series.
H. We can decide whether this series converges by comparison with a geometric series.
I. Partial sums of the series telescope.
J. The terms of the series do not have limit zero.
K. None of the above reasons applies to the convergence or divergence of the series.
1. ∑n=1∞7+sin(n)n
2. ∑n=1∞(2n+4)!(n!)2
3. ∑n=1∞cos2(nπ)nπ
4. ∑n=1∞cos(nπ)nπ
5. ∑n=1∞1nn
6. ∑n=2∞1nlog(5+n)
A. The series is absolutely convergent.
B. The series converges, but not absolutely.
C. The series diverges.
D. The alternating series test shows the series converges.
E. The series is a p-series.
F. The series is a geometric series.
G. We can decide whether this series converges by comparison with a p series.
H. We can decide whether this series converges by comparison with a geometric series.
I. Partial sums of the series telescope.
J. The terms of the series do not have limit zero.
K. None of the above reasons applies to the convergence or divergence of the series.
1. ∑n=1∞7+sin(n)n
2. ∑n=1∞(2n+4)!(n!)2
3. ∑n=1∞cos2(nπ)nπ
4. ∑n=1∞cos(nπ)nπ
5. ∑n=1∞1nn
6. ∑n=2∞1nlog(5+n)
Transcribed Image Text:For each of the series below select the letter from a to c that best applies and the letter from d to k that best applies. A possible answer is af, for example.
A. The series is absolutely convergent.
B. The series converges, but not absolutely.
C. The series diverges.
D. The alternating series test shows the series converges.
E. The series is a p-series.
F. The series is a geometric series.
G. We can decide whether this series converges by comparison with ap series.
H. We can decide whether this series converges by comparison with a geometric series.
I. Partial sums of the series telescope.
J. The terms of the series do not have limit zero.
K. None of the above reasons applies to the convergence or divergence of the series.
7+ sin(n)
1.
Vn
(2n + 4)!
(n!)2
cos (n7)
cos(nn)
5.
nyn
1
6.
n log(5 + n)
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