be a POSITIVE sequence. Which of the following statements must be true? Select all the correct answers. Let {an} n=0 O IF the sequence is bounded above, THEN it is convergent. O IF the sequence is not bounded, THEN it is divergent. O IF the sequence is convergent, THEN it is bounded. O IF the sequence is bounded, THEN it is eventually monotonic. O IF the sequence is non-decreasing, THEN it is convergent. O IF the sequence is non-increasing, THEN it is convergent.
be a POSITIVE sequence. Which of the following statements must be true? Select all the correct answers. Let {an} n=0 O IF the sequence is bounded above, THEN it is convergent. O IF the sequence is not bounded, THEN it is divergent. O IF the sequence is convergent, THEN it is bounded. O IF the sequence is bounded, THEN it is eventually monotonic. O IF the sequence is non-decreasing, THEN it is convergent. O IF the sequence is non-increasing, THEN it is convergent.
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter4: Vector Spaces
Section4.2: Vector Spaces
Problem 48E: Let R be the set of all infinite sequences of real numbers, with the operations...
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Transcribed Image Text:Let {an}
be a POSITIVE sequence.
Which of the following statements must be true?
Select all the correct answers.
IF the sequence is bounded above, THEN it is convergent.
IF the sequence is not bounded, THEN it is divergent.
IF the sequence is convergent, THEN it is bounded.
O IF the sequence is bounded, THEN it is eventually monotonic.
O IF the sequence is non-decreasing, THEN it is convergent.
O IF the sequence is non-increasing, THEN it is convergent.
U
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