(j) 5″ n! π
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:**Exercise: Monotonic Sequences**
**Question:**
Which of the following sequences are eventually monotone (or strictly) increasing (or decreasing)? Justify your answers, assuming the usual properties of trigonometric functions where necessary.
**Sequences:**
(a) \(\left\{\frac{(-1)^n}{n}\right\}\)
(b) \(\left\{n - \frac{1}{n}\right\}\)
(c) \(\left\{n + \left(\frac{(-1)^n}{n}\right)\right\}\)
(d) \(\left\{n^2 - 10n + 100\right\}\)
(e) \(\left\{2 + (-1)^n\right\}\)
(f) \(\left\{\frac{3n^2 + (-1)^n}{n}\right\}\)
(g) \(\left\{\sin \frac{n\pi}{2}\right\}\)
(h) \(\left\{\sin n\pi\right\}\)
(i) \(\left\{\frac{n}{2n}\right\}\)
(j) \(\left\{\frac{5^n}{n!}\right\}\)
(k) \(\left\{\cos \frac{\pi}{2n}\right\}\)
(l) \(\left\{\sin \frac{\pi}{3n}\right\}\)
(m) \(\left\{\frac{3n + 5}{n^2 - n - 2}\right\}\)
(n) \(\left\{\frac{1}{\sqrt{n}} - \frac{1}{\sqrt{n+1}}\right\}\)
Expert Solution
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