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1b. Show that lim inf (n) = = -∞ if and only if {n} is not bounded below.

1b. Show that lim inf (n) = = -∞ if and only if {n} is not bounded below.

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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1b. Show that lim inf (n) = -∞ if and only if {n} is not bounded below. : Argue that if {n} is not bounded below then lim inf (x₂) =1∞ Show that if lim inf (x) = ∞ then {n} is not bounded below. Hint: Suppose that {n} is bounded below (i.e., there is M € R, such that, M ≤ xn, for all n = N)
Transcribed Image Text:1b. Show that lim inf (n) = -∞ if and only if {n} is not bounded below. : Argue that if {n} is not bounded below then lim inf (x₂) =1∞ Show that if lim inf (x) = ∞ then {n} is not bounded below. Hint: Suppose that {n} is bounded below (i.e., there is M € R, such that, M ≤ xn, for all n = N)
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