For each of the series below select the letter from a to c that best applies and
ID: 3211594 • Letter: F
Question
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)lim from n=1 to infinity
[5+sin(n)] / [n^(1/2)]
2)lim from n=1 to infinity
[ cos^(2) (npi) ] / [npi]
3) [cos(npi)] / [npi]
**please show work and explain on how to get to answer, & which tests to use, to understand**
Explanation / Answer
1)
2)since cos^2(npi) is always 1 for all values,thus given series becomes a harmonic progression
ans = C,J
3)since cos(npi) is 1 for even n and -1 for odd n
given series becomes a difference of 2 harmonic progressions and hence same answer as before Ans = C,J
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