Consider the following six sequences: Cn = n², dn 6n + 4 7n 3' Wn = n Un - = (-²) * · (27). —2)", Zn = n cos Vn = (−1)” + For each of these six sequences, answer the following questions: (a) Give an example of a monotone subsequence. (b) Give its set of subsequential limits. (c) Give its lim sup and lim inf. (d) Is it bounded? 1/4 n
Consider the following six sequences: Cn = n², dn 6n + 4 7n 3' Wn = n Un - = (-²) * · (27). —2)", Zn = n cos Vn = (−1)” + For each of these six sequences, answer the following questions: (a) Give an example of a monotone subsequence. (b) Give its set of subsequential limits. (c) Give its lim sup and lim inf. (d) Is it bounded? 1/4 n
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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Question
Transcribed Image Text:Consider the following six sequences:
Cn = n²,
dn
6n + 4
7n 3'
Wn
=
n
Un
- = (-²) * ·
(27).
—2)", Zn = n cos
Vn = (−1)” +
For each of these six sequences, answer the following questions:
(a) Give an example of a monotone subsequence.
(b) Give its set of subsequential limits.
(c) Give its lim sup and lim inf.
(d) Is it bounded?
1/4
n
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