(1) Suppose that (an) tends to infinity. (a) Suppose that (bn) tends to minus infinity. What can you determine about the sequence (anbn) as n goes to infinity? (b) Suppose the sequence (cn) is convergent. What can you determine about the sequence (anCn) as n goes to infinity (-hint: this will depend on what (Cn) converges to!) (c) Considering Proposition 6.4.3, we might think that this could be generalised to any sequence (xn) which contains a bounded subsequence. Explain why this does not in fact generalise the stated result.
(1) Suppose that (an) tends to infinity. (a) Suppose that (bn) tends to minus infinity. What can you determine about the sequence (anbn) as n goes to infinity? (b) Suppose the sequence (cn) is convergent. What can you determine about the sequence (anCn) as n goes to infinity (-hint: this will depend on what (Cn) converges to!) (c) Considering Proposition 6.4.3, we might think that this could be generalised to any sequence (xn) which contains a bounded subsequence. Explain why this does not in fact generalise the stated result.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.3: Geometric Sequences
Problem 81E
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Question
![(1) Suppose that (an) tends to infinity.
(a) Suppose that (bn) tends to minus infinity. What can you determine about
the sequence (anbn) as n goes to infinity?
(b) Suppose the sequence (cn) is convergent. What can you determine about the
sequence (anCn) as n goes to infinity (-hint: this will depend on what (Cn)
converges to!)
(c) Considering Proposition 6.4.3, we might think that this could be generalised
to any sequence (xn) which contains a bounded subsequence. Explain why
this does not in fact generalise the stated result.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb7f27c73-756c-4a47-8ea7-79b047cfb8fe%2F07c48bb5-0240-4301-b866-4a7335fd3aa2%2Fr0lefdc_processed.jpeg&w=3840&q=75)
Transcribed Image Text:(1) Suppose that (an) tends to infinity.
(a) Suppose that (bn) tends to minus infinity. What can you determine about
the sequence (anbn) as n goes to infinity?
(b) Suppose the sequence (cn) is convergent. What can you determine about the
sequence (anCn) as n goes to infinity (-hint: this will depend on what (Cn)
converges to!)
(c) Considering Proposition 6.4.3, we might think that this could be generalised
to any sequence (xn) which contains a bounded subsequence. Explain why
this does not in fact generalise the stated result.
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