(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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