Let (an) be a sequence of positive numbers, S = {am:n E N}, and c E R a given number. A. If (an) converges to L E R, 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 a, É B(L,1). B. If (an) is increasing and S is bounded below then (an) is convergent C. If (an) is bounded, then it is convergent D. If (an) is increasing and an > 1 for all n, then (an) is convergent E. If (am) is decreasing then c 오 is - an

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Let (an) be a sequence of positive numbers,
S = {an:n E N}, and c E R a given
number.
A. If (an) converges to LE R, 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 (an) is increasing and S is bounded
below then (an) is convergent
C. If (an) is bounded, then it is convergent
D. If (an) is increasing and an > 1 for all n,
then (an) is convergent
E. If (an) is decreasing then c
1 is
an
increasing
Transcribed Image Text:Let (an) be a sequence of positive numbers, S = {an:n E N}, and c E R a given number. A. If (an) converges to LE R, 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 (an) is increasing and S is bounded below then (an) is convergent C. If (an) is bounded, then it is convergent D. If (an) is increasing and an > 1 for all n, then (an) is convergent E. If (an) is decreasing then c 1 is an increasing
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