(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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