Let (an) and (bn) be bounded nonnegative sequences. (a) Prove that lim sup anbn ≤ lim sup an lim sup bn. n+x0 n+x0 00+u (b) Give an example of sequences where the inequality in Part (a) is strict. (c) Give an example of sequences (so not necessarily nonnegative) in which the inequality of Part (a) fails.

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