Let (sn) be a sequence with lim sup sn = 10 and lim inf sn = 5. (a) Show that (sn) is bounded. (b) Construct a sequence (sn) with lim sup sn = 10 and lim inf sn = 5 and with infinitely many subsequential limits. (It is redundant to say this but just to emphasize: you need to prove that your constructed sequence has infinitely many subsequential limits and that lim sup sn = 10 and lim inf sn = 5.

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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.