Let (an) be a bounded sequence. (a) Prove that the sequence defined by yn = sup{ak : k ≥ n} converges. (b) The limit superior of (an), or lim sup an, is defined by                                   lim sup an = lim yn, where yn is the sequence from part (a) of this exercise. Provide a reasonabledefinition for lim inf an and briefly explain why it always exists forany bounded sequence.

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Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence.  It was invented by German mathematician Carl Friedrich Gauss.