2 Give examples of sequences, one in each case, of the following. (a) (an) is unbounded and not monotone. (b) (a,) and (b,) are not convergent, but (2a, – 3b,) is convergent. (c) (an) is convergent but not monotone.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.3: Geometric Sequences
Problem 18E
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If a question says to 'use the definition' to prove some result, your answer must rely solely on the
definition to prove the result, and not on other results from the course.
If the question does not say this then you may use any result from the course in your answer.
Transcribed Image Text:If a question says to 'use the definition' to prove some result, your answer must rely solely on the definition to prove the result, and not on other results from the course. If the question does not say this then you may use any result from the course in your answer.
2 Give examples of sequences, one in each case, of the following.
(a) (an) is unbounded and not monotone.
(b) (a,) and (b,) are not convergent, but (2a, - 3b,) is convergent.
(c) (an) is convergent but not monotone.
(d) (an) is not convergent but (a,(a, - 2)) is convergent.
Transcribed Image Text:2 Give examples of sequences, one in each case, of the following. (a) (an) is unbounded and not monotone. (b) (a,) and (b,) are not convergent, but (2a, - 3b,) is convergent. (c) (an) is convergent but not monotone. (d) (an) is not convergent but (a,(a, - 2)) is convergent.
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