(6) For each of the following parts, answer whether the sequence is bounded, whether it is monotone, and whether it converges to a real number, diverges to +oo or -0o, or diverges. So, for each part, give three answers and explain. You do not need to give proofs using the definition of limit, but if you wish to use a theorem from class you should state the result and explain how it applies. (a) Sn = = cos(플) (b) Sn = 12 – (c) Sn = -n2 = -n? %3D
(6) For each of the following parts, answer whether the sequence is bounded, whether it is monotone, and whether it converges to a real number, diverges to +oo or -0o, or diverges. So, for each part, give three answers and explain. You do not need to give proofs using the definition of limit, but if you wish to use a theorem from class you should state the result and explain how it applies. (a) Sn = = cos(플) (b) Sn = 12 – (c) Sn = -n2 = -n? %3D
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:For each of the following parts, answer whether the sequence is bounded, whether it is monotone, and whether it converges to a real number, diverges to \(+\infty\) or \(-\infty\), or diverges.
So, for each part, give three answers and explain. You do not need to give proofs using the definition of limits, but if you wish to use a theorem from class you should state the result and explain how it applies.
(a) \( s_n = \cos \left( \frac{n\pi}{2} \right) \)
(b) \( s_n = 12 - \frac{1}{n^3} \)
(c) \( s_n = -n^2 \)
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