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an = (-1)", bn Cn = n² dn= n (a) For each sequence, give an example of a monotone subsequence. 6n + 4 7n-3 -

an = (-1)", bn Cn = n² dn= n (a) For each sequence, give an example of a monotone subsequence. 6n + 4 7n-3 -

Advanced Engineering Mathematics
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
The text describes four sequences and asks for a monotone subsequence for each. Here are the sequences: 1. \( a_n = (-1)^n \) 2. \( b_n = \frac{1}{n} \) 3. \( c_n = n^2 \) 4. \( d_n = \frac{6n + 4}{7n - 3} \) **(a) For each sequence, give an example of a monotone subsequence.** Each sequence presents different characteristics: - \( a_n \) alternates between -1 and 1. - \( b_n \) is a decreasing sequence as \( n \) increases. - \( c_n \) is an increasing sequence as \( n \) increases. - \( d_n \) involves more complex rational functions, which can also exhibit monotonic behavior under specific conditions.
Transcribed Image Text:The text describes four sequences and asks for a monotone subsequence for each. Here are the sequences: 1. \( a_n = (-1)^n \) 2. \( b_n = \frac{1}{n} \) 3. \( c_n = n^2 \) 4. \( d_n = \frac{6n + 4}{7n - 3} \) **(a) For each sequence, give an example of a monotone subsequence.** Each sequence presents different characteristics: - \( a_n \) alternates between -1 and 1. - \( b_n \) is a decreasing sequence as \( n \) increases. - \( c_n \) is an increasing sequence as \( n \) increases. - \( d_n \) involves more complex rational functions, which can also exhibit monotonic behavior under specific conditions.
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