Let (un) and (Vn) be two sequences defined by n + "n Un+1 Un + Vn 0 < v1 < U1, Un+1 Un + Vn 2 (a) Show that (um) and (vn) are monotonic sequences. (b) Show that (un) and (vn) converge to the same limit.

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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.