re true (there might be more than one true statement). converges to x ER then liminf(x)

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.3: Geometric Sequences
Problem 16E
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Mark all statements that are true (there might be more than one true statement).
If a real sequence {x} converges to x E R then liminf(x) <x<limsup(x) .
Let {x}
If x is a cluster point of {x}, then liminf(x) <x<limsup(x).
n
Let {x}
be a sequence of real numbers. Then limsup(x)=∞ if and only if {x} is not bounded above.
Let {x}
be a sequence of real numbers. If M ≤x, for all n € N, then M ≤ liminf(x).
n
be a sequence of real numbers. Then liminf(x)=-∞ if and only if {x} is not bounded above.
n
Transcribed Image Text:Mark all statements that are true (there might be more than one true statement). If a real sequence {x} converges to x E R then liminf(x) <x<limsup(x) . Let {x} If x is a cluster point of {x}, then liminf(x) <x<limsup(x). n Let {x} be a sequence of real numbers. Then limsup(x)=∞ if and only if {x} is not bounded above. Let {x} be a sequence of real numbers. If M ≤x, for all n € N, then M ≤ liminf(x). n be a sequence of real numbers. Then liminf(x)=-∞ if and only if {x} is not bounded above. n
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