Let (an) be a sequence of positive numbers, S = {an:n E N}, and c E Ra given %3D number. A. If (am) converges to LE R, then there is only a finite number of indices n EN such that the condition lan - L| <1 is not satisfied, i.e. such that an É B(L, 1). B. If (a,) is increasing and S is bounded below then (an) is convergent C. If (a,) is increasing and a, > 1 for all n, then (an) is convergent D. If (an) is decreasing then c – is an increasing E. If (a,) is bounded, then it is convergent

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Let (an) be a sequence of positive numbers,
S = {an:n E N}, and c E Ra given
%3D
number.
A. If (am) converges to LER, then there is
only a finite number of indices n EN such
that the condition |an – L| <1 is not
satisfied, i.e. such that an É B(L, 1).
-
B. If (a,) is increasing and S is bounded
below then (an) is convergent
C. If (a,) is increasing and a, > 1 for all n,
then (an) is convergent
D. If (an) is decreasing then c –
is
an
increasing
E. If (a,) is bounded, then it is convergent
Transcribed Image Text:Let (an) be a sequence of positive numbers, S = {an:n E N}, and c E Ra given %3D number. A. If (am) converges to LER, then there is only a finite number of indices n EN such that the condition |an – L| <1 is not satisfied, i.e. such that an É B(L, 1). - B. If (a,) is increasing and S is bounded below then (an) is convergent C. If (a,) is increasing and a, > 1 for all n, then (an) is convergent D. If (an) is decreasing then c – is an increasing E. If (a,) is bounded, then it is convergent
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