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.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.2: Arithmetic Sequences
Problem 64E
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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
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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